Papers

In the framework of multiple orthogonal polynomials (MOPs) and their extension to the multivariate setting, a unified mechanism for generating structured families of multiple orthogonal polynomials across diverse multidimensional domains is still lacking. In this work, we bridge this gap by developing an extended Koornwinder-type methodology for constructing multivariate multiple orthogonal polynomials. We introduce two distinct coupling schemes: combining a univariate MOPs family with a standard orthogonal family, which enables the definition of both Type I and Type II bivariate systems along with their dual biorthogonality relations, and coupling two univariate MOPs families to form Type II multivariate systems. Using this general framework, we provide the first explicit formulations of multiple orthogonal polynomials on a variety of bivariate regions, including bounded domains such as a parabolic domain and the square $[0,1]^2$, non-standard unbounded geometries like the positive quadrant $(\mathbb{R}_0^+)^2$ and the wedge $\mathbb{V}^2$, as well as new constructions on the triangle $T$. Furthermore, explicit multiple orthogonal systems on the $d$-dimensional simplex $T^d$ and on the $d$-dimensional cone $\mathbb{V}^d$ are given.

Reinforcement learning is now central to eliciting reasoning in large language models, while in the popular algorithm Group Relative Policy Optimization (GRPO) every token in a rollout receives the same advantage. We ask how to make process supervision efficient: accelerating convergence and improving final quality without the cost of value networks. We propose Bag-of-Tokens Group Relative Policy Optimization (BoT-GRPO), which extends GRPO to token-level reward models through a length-invariant "bag of tokens" aggregation: it collects all token-level rewards across rollouts, weights each by the inverse of its source sequence length, and computes per-token advantages relative to weighted group statistics. BoT-GRPO is critic-free, and is a drop-in replacement wherever GRPO is used when token-level reward is available. On React front-end code generation, BoT-GRPO reaches $80\%$ compile rate up to $1.9\times$ faster than GRPO and converges faster than modern GRPO variants (GSPO, DAPO, PURE) while reaching higher final compile and VLM-judged win rates. On a second task, AIME mathematical reasoning, BoT-GRPO delivers absolute Pass@$k$ gains up to $8.1\%$ over GRPO in half the steps. For both tasks we compare the algorithm's performance on reasoning vs. non-reasoning base-model families (Qwen2.5-3B, SmolLM3-3B, Phi-4-mini-reasoning). Our experiments also yield a practical recipe for the reward model itself: reward stability matters more than richness: clean, bounded, stable fine-grained signals consistently accelerate learning where noisier alternatives stall.

Low surface brightness galaxies (LSB-galaxies) and the outer regions of disks of "normal" surface brightness galaxies (HSB-galaxies) are compared in terms of the radial distributions of star formation rates and efficiencies, as well as the Toomre stability parameter $Q_T$, using data from several samples of galaxies with high $HI$ content. It is shown that the dependences of the star formation rate $SFR$ on the $HI$ surface density and the star formation efficiency $SFE$ on the disk optical brightness $\mu_g$ for LSB- and HSB-galaxies have a similar character, suggesting similarity in the conditions that determine the star formation rate in low gas density regions. The considered dependences persist out to distances corresponding to brightnesses of 26-27 mag/arcsec$^2$, where the expected volume density of the equilibrium gas layer should be very low. It is suggested that the disk density at large distances from the center may be significantly underestimated.

Concept-based vision models represent images through an intermediate layer of human-inspectable concepts, so what a model relies on can be traced to those concepts. However, those models are often limited to fixed categories or depend on language to define their concepts. We introduce DisParQ (Discrete Parts with Quantized attributes), a method that learns spatially grounded, discrete concept representations from a powerful frozen vision-only self-supervised backbone. It requires no class labels and no language supervision. Each image patch is assigned to exactly one concept from a learnable prototype dictionary, and only a sparse subset of concepts may activate per image. To capture how each concept varies across images (e.g., the type of a "wheel"), we learn continuous residuals alongside the concepts and then quantize them into discrete attributes. A spatial decoder reconstructs the backbone's representation from the concepts and attributes alone, so successful reconstruction means that the discrete representation preserves the backbone's information. We evaluate DisParQ across seven datasets, from general recognition (ImageNet, PartImageNet, Places) to fine-grained benchmarks (CUB, Cars, Dogs, Flowers). We show that DisParQ closely matches its frozen DINOv2 teacher on ImageNet linear probing (83.2% top-1), achieves higher concept consistency than language-aligned models, remains competitive on fine-grained recognition, and enables cross-category part-based retrieval.

Statistical inference under adaptively collected data is becoming increasingly popular across e-commerce and mobile health. Many methods exist for discrete action settings, ranging from weighting to debiasing approaches. Despite the ubiquity of continuous actions in experimentation from optimal pricing to precision dosing, to the best of our knowledge, methods that support statistical inference under continuous action, adaptively collected data remain underdeveloped. In this work, we extend kernel-smoothed doubly robust estimation from i.i.d. data to adaptively collected data with continuous actions. We study a family of adaptively weighted estimators, establish their mean squared error rates, asymptotic normality, and characterize an estimation lower bound as a function of regret. We conclude with recommendations for experimental design informing efficiency and regret, and support our theory with an extensive simulation study.

Surgical video generation holds substantial potential for surgical education, simulation, and data augmentation, yet generating surgical videos with realistic and clinically plausible motion remains challenging. Most existing methods rely on auxiliary conditions, such as masks, trajectories, depth, or reference videos, to achieve visually plausible synthesis. Yet, these auxiliary conditions typically require additional manual annotation or specialized acquisition, making it difficult to scale such methods beyond small, curated datasets. This motivates the need for a reference-free architecture capable of generating high-quality surgical video without requiring auxiliary visual conditions at inference time. We propose FLAIR, a Flow-guided LatentAction Injection framework for Reference-free surgical video generation. FLAIR learns action priors from optical flow of real surgical videos, dynamically predicts corresponding latent action representation from an input prompt, and injects it into a frozen base model to generate surgical videos with improved action consistency. We further construct SurgActionClip-30K, the first large-scale surgical vision dataset comprising action-centric segmented clips and structured caption labels, addressing the persistent lack of fine-grained, action-centric surgical datasets. Lastly, we introduce SurgMetrics, the first surgical domain-specific evaluation metrics for quantifying the quality of generated surgical videos, addressing the persistent absence of clinically grounded evaluation standards in this domain. Extensive experiments demonstrate that FLAIR enables generating high-quality surgical videos using text-only inference without auxiliary conditions, and validation in SurgMetrics demonstrates its strength in alignment with human perception compared to traditional metrics.

A previous work [H. Yamase and M. Zafur, Phys. Rev. B 103, 224527 (2021)] showed that the longitudinal spin susceptibility exhibits a jump when the superconductivity develops continuously inside a magnetic phase. That analysis employed a minimal model containing magnetic and superconducting interactions. However, in correlated-electron systems, both magnetic and bond-charge interactions originate from the same underlying spin-spin exchange interaction. We therefore extend the model by including the uniform bond-charge order to provide a more realistic description of the system. We find that the jump of the longitudinal spin susceptibility remains robust even in the presence of uniform bond-charge order, but the uniform bond-charge order quantitatively enhances the longitudinal spin susceptibility and the size of the jump at $T_c$.

The Color-of-Money (CoM) problem is a financial optimization challenge in which enterprises must determine how to allocate and route funds across multiple accounts, currencies, and time periods while satisfying regulatory, operational, and liquidity constraints. As the number of assets, obligations, and planning periods increases, the decision space grows rapidly, making large-scale optimization increasingly challenging for classical approaches. In this work, we present a proof-of-concept quantum implementation of the CoM problem using IBM Quantum hardware. The original optimization problem is formulated as a constrained Mixed-Integer Linear Programming (MILP) problem and transformed into a Quadratic Unconstrained Binary Optimization (QUBO) representation suitable for quantum execution. We employ a Variational Quantum Algorithm (VQA) with Pauli Correlation Encoding (PCE), a qubit efficient encoding technique and apply error-mitigation technique to improve solution fidelity on noisy quantum hardware. A prototype instance consisting of 3 assets, 3 obligations, and 2 time periods was executed on real IBM quantum hardware and benchmarked against classical exact solver SCIP. The quantum approach successfully reproduced the same optimal solution obtained classically, validating the correctness and feasibility of the proposed methodology. While current noisy quantum hardware does not outperform classical optimization on the evaluated small instance, the results demonstrate the feasibility of executing treasury optimization workloads on current quantum hardware and provide a foundation for future investigations.

We present a new class of structure-preserving, arbitrarily high-order accurate space-time schemes using unstructured simplicial meshes in space for a class of nonlinear acoustic wave propagation systems, in which the nonlinearity is encoded in the constitutive relations between the state and dual variables, while the differential operators retain the standard first-order acoustic wave structure. At the fully discrete level, the schemes satisfy the following properties: I) local conservation of the state variables; II) a local energy/entropy balance on each space-time element, with a consistent, single-valued numerical energy/entropy flux and nonnegative local energy/entropy dissipation, and exact energy conservation when the stabilization terms are omitted; III) weak preservation of the curl involution of the velocity field, even in the presence of discontinuities and with the shock-capturing terms activated. The key ingredients of the new schemes are: i) a discontinuous Galerkin (DG) discretization in space, in which the dual variables are computed as the L2 projections onto the DG space of the energy derivatives with respect to the conserved variables; ii) numerical fluxes and a bubble-weighted, element-local viscous regularization expressed in terms of the dual variables; iii) a continuous-discontinuous Petrov-Galerkin method in time. Properties I)-III) are first proved mathematically and are then verified by suitable numerical tests.

Oblivious transfer (OT) is a fundamental cryptographic primitive that is useful for realizing any two-party computation. Since information-theoretically secure perfect OT is impossible classically and quantumly, research has focused on imperfect protocols, exploring how close to perfect one can get against unbounded dishonest parties. While current approaches often make use of pure quantum states, recent work suggests that mixed quantum states may improve performance. In this paper, we investigate the use of mixed quantum states in Rabin oblivious transfer, where a sender holds one bit and a receiver learns its value with a certain probability while the sender remains ignorant of whether the receiver learned it. We present three mixed-state protocols constructed with two distinct methods, extending an existing pure-state scheme and employing a probabilistic approach, and demonstrate improved performance compared to classical and quantum pure-state protocols across varying parameters.

The demand for personalized LLMs is shifting from style imitation toward content quality. We investigate whether self-distillation can bridge this gap in existing fine-tuning paradigm. To address this limitation, we introduce MIRROR(Meta- personalization by Internalizing Reference-Revealed On-policy Reflections), a novel self-distillation framework that shifts LLM personalization from imitation toward preference internalization. First, we replace reference-token imitation with reference-revealed on-policy self-distillation, aligning the model's next-token distributions along its own generation trajectories with those of its reference-conditioned self, thereby internalizing user preferences rather than reproducing reference wording.Second, we introduce MIRROR-F, a focal plug-in that augments on-policy distributional alignment with selective supervision over informative reference tokens, thereby strengthening content generation while preserving user-specific expression. Across three personalized generation benchmarks, two model scales, and complementary reference-based and LLM-based evaluations, MIRROR and MIRROR-F achieve leading overall personalization performance and superior text quality, while exhibiting less catastrophic forgetting than SFT-based baselines on three unseen personalized generation tasks. The gains are consistent across model scales and application scenarios, translating to improved performance in LLM personalization tasks.

The main result of the paper states that if $0\neq v\in\mathbb C^m\otimes\mathbb C^n$, $d=\min\{m,n\}$, and $p=SR(v)$, then for every $1\le q\le d$, \begin{equation*} \min\left\{OSR(\mathbf U): \begin{array}{l} \mathbf U\in\mathbb M_m\otimes\mathbb M_n\text{ is unitary}, SR(\mathbf Uv)=q \end{array}\right\} = \left\lceil\max\left\{\frac pq,\frac qp\right\}\right\rceil . \end{equation*} Here $OSR(\mathbf U)$ denotes the operator Schmidt rank of $\mathbf U$. Furthermore, if $\mathbf U\in\mathbb M_m\otimes\mathbb M_n$ is unitary and $OSR(\mathbf U)\le k$, then, for every unit vector $x\in\mathbb C^m\otimes\mathbb C^n$ and every $1\le r\le d$, \begin{equation*} F_{\min\{kr,d\}}(\mathbf Ux)\ge F_r(x) \quad\text{and}\quad F_{\min\{kr,d\}}(x)\ge F_r(\mathbf Ux), \end{equation*} where $F_r(x)$ denotes the sum of the $r$ largest squared Schmidt coefficients of $x$. This result is stronger than rank reachability as it controls the entire cumulative Schmidt profile. We also establish a majorization relation and use it to obtain sharp bounds on Schatten-norm distortion and on the change of Rényi entropies under unitaries with bounded operator Schmidt rank.

Guardrails for tool-using LLM agents are usually application-specific rules, which makes multi-step, data-dependent safety policies hard to specify, audit and reuse. As a declarative alternative, we evaluate metric first-order temporal logic (MFOTL), replaying the recorded trajectories that AgentDojo, STAC and R-Judge already ship through the unmodified MonPoly monitor, offline and without running an agent. On these corpora, five generic obligations flag 71.8% of STAC attack chains and 70.1% of successful AgentDojo attacks, but also fire on 29.3% of benign runs. This imprecision stems from the corpora rather than the logic: they rarely record approvals and never record timestamps, so history-dependent obligations reduce to detecting risky action types. Where the trace does carry relational context, provenance-aware policies discriminate better; that context, however, is itself attackable, and one planted line defeats a naive provenance check on 94-99% of the runs it would otherwise flag. Binding provenance to the lookup that produced it closes this evasion at no cost in detection or benign firing. Taken together, these results show that formal temporal monitoring adds value exactly when the trace exposes trustworthy history. We therefore quantify how far current benchmarks are from that point and propose a twelve-field enforcement-ready trace schema.

Electroencephalography (EEG) is highly susceptible to electromyographic (EMG) artifacts, whose temporal heterogeneity and spatial-spectral overlap with neural activity can leave mixed sources after blind source separation. Existing artifact-removal methods are further limited by scarce reliable component-level ground truth: expert annotations are costly and subjective, while no established method provides realistic simulation-based ground truth for EMG contamination in multichannel scalp EEG. To address these limitations, we propose a framework combining a frequency-aware high-dimensional representation with Multi-Instance Learning. The representation unfolds separated components into frequency-resolved intra-components, creating a space in which mixed neural and muscular activity becomes more separable, while the weakly supervised learning formulation enables artifact-likelihood scores for individual intra-components to be learned from epoch-level labels without finer-grained ground truth. The resulting intra-component classifier supports fine-grained EMG artifact detection and score-guided attenuation. Experiments on held-out subjects show that the framework learns informative intra-component scores and reduces artifact-related spectral deviations most clearly for jaw tension, with moderate effects for raising eyebrows and limited effects for frowning.

Head avatar modeling requires jointly optimizing multiple objectives with different dominant effects on geometry, appearance, and cross-view consistency. However, their relative effectiveness varies across training states, while existing pipelines typically rely on fixed loss weights or handcrafted stage-wise schedules. A central challenge is therefore to identify which optimization direction is more beneficial at each training state. We propose a counterfactual route optimization framework for Gaussian head avatar modeling, which characterizes state-dependent optimization preference from the realized effects of alternative updates rather than predefined heuristic weighting. Starting from the same training state, we perform short-horizon route-restricted lookahead over geometry, appearance, and joint update routes and evaluate their outcomes under a unified utility. The resulting counterfactual evidence is factorized into a geometry–appearance preference and a residual joint advantage, separately capturing the relative preference between individual update directions and the additional benefit of coordinated optimization. We further amortize this offline evidence into a lightweight controller that directly estimates the current optimization preference and applies bounded modulation to the training objectives during full avatar optimization. Experiments on the NeRSemble dataset validate the effectiveness of the proposed design, consistently outperforming existing methods while preserving clearer local facial structures and finer details.

For a positive real lacunary sequence and any probability measure $\mu$ with polynomial Fourier decay, we determine, for $\mu$-almost every $x$, the asymptotic maximal volume of convex bodies avoiding the first $N$ dilates of $x$ modulo $\mathbb Z^d$. Among homothets of a fixed convex body, the maximal volume is asymptotic to $(\log N)/N$. When all convex bodies in the unit cube are allowed, it is asymptotic to $d(\log N)/N$. For independent uniform points in a fixed convex body $\Omega\subset\mathbb R^d$, the maximal volume of an empty convex body is asymptotic to $d\operatorname{vol}(\Omega)(\log N)/N$ almost surely. We also show, by constructing a one-dimensional counterexample, that lacunarity cannot be replaced by sparsity on sublacunary scales.

Cooperative behavior can improve environmental quality, whereas selfish defection can degrade shared resources. In a recent agent-based study of the Aksum civilization (Vasellini et al., 2025), a population of agents moving over a reconstructed landscape and playing a local Public Goods Game grew faster and peaked higher when the game was enabled, but settled, in the long run, at the same population level as when it was not. Here we show that this behavior does not depend on the many rules of that model. We develop a theoretical ecological model of three coupled discrete-time equations, in which two sub-populations grow logistically and share a carrying capacity that rises when cooperators are sufficiently numerous and decays otherwise. Without fitting any parameter to the simulation, the equations reproduce its qualitative behavior: an initial boom, damped oscillations, and stabilization; a higher peak when the cooperative mechanism is active; and a final equilibrium that does not depend on it. Cooperation can be self-sustained for a transient period, but in the absence of measures that mitigate free-riding it collapses, and the environmental gains it produced are lost with it.

Reward modeling often requires jointly representing and reasoning over multiple evaluation criteria, yet verbalizing this process token by token can incur substantial inference cost. Recent work on latent reasoning suggests that continuous states may support this computation more compactly. We introduce LatentGRM, a latent evaluation framework built on semantic chunking, compression, and reconstruction. By using the structure of rubric-guided evaluations to guide compression, LatentGRM learns compact continuous trajectories that support autonomous pairwise judgments without generating textual assessments. A separate interpreter reconstructs evaluation text from these trajectories, providing an offline view of the information retained under compression. Under matched training data and backbones, LatentGRM achieves competitive aggregate preference accuracy relative to explicit Supervised Fine-Tuning (SFT) judges at both 4B and 8B scales. Across four benchmark domains, LatentGRM-8B compresses evaluation trajectories by 8.9–9.2x and reduces total judge inference time by 6.1–7.0x at vote@5. Controlled rubric interventions show that criterion-dependent preference information is carried through the latent sequence. Together, these results demonstrate that continuous latent evaluation can substantially reduce inference cost while preserving competitive judgment quality.

As in all fields of engineering, control engineers constantly face a dichotomy between achieving high performance and the limited availability of resources for sensing, actuation, and control. This tension often translates into formalizing design problems with sparsity constraints; that is, the design involves decision variables whose number, spatial reach, temporal spread, or other physical expressions are much smaller than in the ideal scenario of unconstrained optimization of a task-related performance metric. Even though this fundamental limitation underlines a plethora of methodological approaches and application domains, the control literature is fragmented into several lines of work tailored to specific scenarios. This survey fills the gap by bringing together several lines of work on handling sparsity in relevant control problems such as actuator scheduling, minimal-energy controllability, maximum hands-off control, and online convex optimization, and weaving a red thread through theoretical foundations and algorithms. Beyond establishing a coherent, structured narrative of problems and solutions for handling sparsity in control scenarios, we discuss open areas and relevant directions for future research, motivated by the growing complexity of control systems and their relations with key domains such as pervasive computing, distributed learning, cyberphysical security, and ecological footprint.

Messaging experiments on high-performance computing clusters must coordinate services, clients, and measurement within scheduler allocations. We present HPC-MQBench, a Slurm-orchestrated benchmark that links resumable experiment control to record checks, delivery accounting, and qualification before rate ranking. Its Kafka evaluation placed producers/controller, one broker, consumers, and monitoring on four nodes. With memory-backed logs, 120 workload configurations yielded 99 qualified observations, 14 outside the producer-delivery policy, and seven with invalid evidence. Two validation stages each repeated ten workloads in five blocks. In the final stage, the selected workload qualified in all five observations, with medians of 2,927 mebibytes per second balanced endpoint rate, 1.24 percent pending deliveries, and 2.56 seconds for the 99th-percentile latency. It qualified in only two observations in the earlier stage, where qualification improved after an allocation boundary without establishing a causal allocation effect. Selection is conditional on the stage and delivery policy. Resource measurements did not isolate a unique bottleneck. The contribution is a framework for distributed experiment control and auditable configuration selection at a fixed broker count; multi-broker support and scaling experiments remain future work.

World models can enable autonomous ultrasound scanning by predicting the outcomes of probe motions from local observations. Learning this action–observation relationship typically relies on synchronized video–pose pairs, which are costly to collect at scale and largely unavailable in routine clinical recordings. Reliable action following further requires modeling ultrasound's cross-sectional sampling geometry. We present UltraWorld, a self-distillation recipe that transfers priors from clinical ultrasound videos into interactive world models without real action annotations. Starting from clinical videos, we adapt a video foundation model into an ultrasound generator conditioned on reference images and anatomical masks. Anatomical masks sampled along programmable trajectories through 3D anatomy provide spatial guidance for synthesizing action–video pairs. We then use these synthetic pairs to self-distill the generator into a world model that predicts future observations from local observations and actions, without requiring anatomical masks or other 3D assets at inference time. To further improve action following, we introduce the Acoustic Sampling Map (AsMap), which represents probe poses and imaging settings as pixel-wise 3D sampling positions, beam directions, and depths. Experiments demonstrate improved prediction fidelity and action following. Across nine simulated closed-loop local planning episodes, UltraWorld reduces the mean final distance to the goal and orientation error by 29% and 38%, respectively, compared with visual servoing. Project Page: https://ultraworld-project.github.io/.

Reliable liver segmentation in contrast-enhanced MRI is essential for quantitative hepatic assessment, treatment planning, and longitudinal disease monitoring. However, limited annotated data and scanner- or vendor-dependent intensity variations can cause overfitting and poor generalization to unseen acquisition domains. Moreover, simultaneously achieving robust global localization and precise boundary delineation remains challenging, while predictions may contain isolated false-positive regions outside the main liver component. To address these challenges, we propose CIRSeg, a coarse-to-fine, intensity-robust liver segmentation framework based on nnU-Netv2. CIRSeg combines 3D CutMix with stochastic intensity transfer using either Nyul augmentation or histogram matching to improve robustness to heterogeneous MRI intensities. Its cascaded architecture decouples low-resolution anatomical localization from full-resolution boundary refinement. At inference, source-free test-time adaptation based on confidence-filtered predictions and probability-prior regularization further improves robustness to out-of-distribution inputs. As a final deterministic post-processing step, largest connected component filtering removes isolated false-positive regions. On the CARE 2026 test set, CIRSeg achieves Dice scores of 97.13% and 97.93% on the in-domain and unseen-domain subsets, with corresponding HD95 values of 20.18 mm and 11.30 mm, respectively. These results demonstrate consistently accurate segmentation across both in-domain and unseen acquisition settings. The code is available at https://github.com/jingkunchen/MICCAI_CARE_2026

Accurate prediction of the electronic properties of extended $\pi$-conjugated systems with radical character remains a major theoretical challenge. To overcome this challenge, thermally-assisted-occupation density functional theory (TAO-DFT) has been developed in recent years. In this study, we employ TAO-DFT to systematically explore the electronic properties of ladder-type phenylenes ($n$-LPs), containing $n$ linearly fused four-membered carbon rings. Our calculations reveal that all investigated $n$-LPs (with $n$ = 1 ~ 40) possess singlet ground states. With increasing $n$-LP length, we observe a transition from the nonradical character of shorter $n$-LPs to the polyradical character of longer $n$-LPs. Notably, we identify a distinct damped periodic oscillation in the radical character of $n$-LPs, featuring highly correlated hotspots at specific lengths ($n = 3k - 1$, where $k$ are positive integers). The real-space representation of active orbitals confirms this global electronic behavior is governed by the intrinsic structural periodicity and completely delocalized nature of the active orbitals along the central ladder framework. These findings provide fundamental insights into the size-dependent electronic properties of $n$-LPs, guiding their rational design for future nanomaterial applications.

Causal discovery becomes particularly challenging when the available sample size is small relative to the number of variables. This challenge also arises in the linear non-Gaussian acyclic model (LiNGAM), an identifiable framework for causal discovery from observational data. DirectLiNGAM estimates a causal order, which arranges variables so that causes precede their effects, by sequentially identifying an exogenous variable and removing its linear effect from the remaining variables. We establish a structural limitation of this procedure: when the number of variables exceeds the sample size, repeated residualization necessarily becomes degenerate before the full causal order can be determined. Our analysis further reveals that each residual can be reconstructed using only a graph-determined subset of variables already placed earlier in the causal order, termed the active boundary. This result motivates AdaPS-LiNGAM (Adaptive Predecessor Selection LiNGAM), which reconstructs each residual directly from the original observations using an adaptively chosen sparse subset of those earlier variables. The same subset-selection principle is also applied to the final pruning step for edge estimation. Experiments on synthetic data demonstrate that AdaPS-LiNGAM provides accurate causal-structure recovery in sample-limited settings and degrades more gradually as the sample size decreases.

Turning a CAD design into an assembly plan is still largely done by hand, requiring engineers to reason about geometric feasibility, tool access, stability, and the ergonomics of human assembly. In this work, we encode long-established design for assembly (DfA) principles into a contained, end-to-end approach for generating assembly plans. Our approach takes only a mesh assembly and produces either a step-by-step assembly manual or a structured failure report, requiring no joint metadata, fastener annotations, or additional information. Four major components of a manufacturing plan are addressed autonomously: an assembly tool list, the assembly sequence and subassemblies, an assembly manual, and design feedback for improving assemblability. For determining the sequence plan, we systematically disassemble the object in a physics simulator and apply a cost function that encodes DfA principles. Manual generation, tool labelling, and assembly feedback rely primarily on multimodal large language models. Compared with a baseline that always removes the outermost part first from Tian et al., DfA-aware sequence planning reduces simulated assembly time, measured with a robot-arm assembly-time proxy, by 35% on 136 assemblies of 5 to 30 parts. The correct tool is selected for 88.6% of assembly steps. A vision-language model judge compares the generated manuals against ablated variants, identifying which page elements carry the information a reader needs. The presented approach and open-source code are available for use by engineers or AI agents looking to rapidly accelerate the creation of manufacturing plans for a given product design.

Diffusion models excel at image synthesis, but they remain limited in their ability to reliably satisfy structured spatial reasoning constraints. In conditional data distribution modeling tasks with implicit logical structure, such as puzzles defined by visible clues paired with consistent solutions, state-of-the-art generative models tend to approximate pixel-space distributions without learning the underlying logical rules required for inference. To address this limitation, we present a novel framework for spatial reasoning with diffusion models that leverages unsupervised object discovery and abstractions of object relations. We show that the relational knowledge derived from object-centric representations enriches diffusion models with structural primitives, allowing them to effectively guide the generative representation space during both training and inference, and enabling conditional image generation that satisfies reasoning constraints. Additionally, we introduce a large-scale generative spatial reasoning benchmark with four datasets inspired by human-solvable puzzles. Our results show that relational abstractions significantly improve reasoning capabilities of diffusion models on a variety of complex reasoning tasks, while enabling robust generalization in out-of-distribution settings.

Mourad E.H. Ismail and Kenneth S. Miller in 1982 conjectured that for $\nu>\mu\geq0$ and $b>a>0$ the function $$x\mapsto G(x;\mu,\nu)=\left(\frac ba\right)^{\mu-\nu}\frac{I_\mu(a\sqrt{x})I_\nu(b\sqrt{x})}{I_\mu(b\sqrt{x})I_\nu(a\sqrt{x})},$$ where $I_\nu$ stands for the modified Bessel function of the first kind, is the Laplace transform of an infinitely divisible probability distribution. Their conjecture is equivalent to the monotonicity property of some exponential sums over the zeros $j_{\nu,n}$ with respect to the order, where $j_{\nu,n}$ denotes the $n$th positive zero of the Bessel function of the first kind of order $\nu$. In this paper our aim is to reduce the problem further to the monotonicity, with respect to $\nu$, of \[Q_\nu(t)=\sum_{n\geq1}j_{\nu,n}^2e^{-t j_{\nu,n}^2},\qquad t>0,\] and to prove this monotonicity. In this way we show that indeed the above function $x\mapsto G(x;\mu,\nu)$ is the Laplace transform of an infinitely divisible probability distribution, and the above conjecture is true. The key ingredient in our proof is an integral representation for the derivative of a quotient of modified Bessel functions of the first kind with respect to the order, combined with Bernstein's theorem and a probability tail argument.

Reproducible benchmarking of Large Language Model (LLM) inference is challenging because repeated measurements can vary with execution and system state. We present the Sequential Isolation Methodology, a controlled benchmarking and regression-testing protocol designed to reduce between-run measurement variance while deliberately varying workload concurrency. We evaluate three representative open-source LLMs on an NVIDIA A100 80GB GPU using vLLM 0.9.1 across six context sizes and eight concurrency levels, with five repetitions per configuration. The final protocol reduces average coefficient of variation (CV) from 15.2% in the least controlled methodology stage to 2.2% under the final protocol; using CV computed across the five repetition-level median (P50) TTFT values per configuration, 113 of 144 configurations (78.5%) achieve CV below 3%. The measurements also show a marked latency transition between 200 and 500 concurrent users on the tested stack and descriptive differences in P99 latency across the three models. We additionally provide an explicit cost break-even model with sensitivity to API pricing. The protocol is intended to provide a stable reference for reproducible comparison and regression testing rather than to predict absolute behavior under uncontrolled production traffic. Infrastructure-as-Code and benchmark scripts support replication of the experimental environment.

Transitioning from a digital design to a robotic assembly process currently requires months of expert manual tuning to reconcile part geometries with robotic constraints. This paper presents an end-to-end, autonomous pipeline for the design and physical construction of bespoke wooden assemblies. A generative AI agent translates user prompts into initial 3D geometries, balancing the visual fidelity of the design with select physical constraints. The assemblability of the design is further improved by a gradient-based repair stage that backpropagates through a graph attention network surrogate to adjust component geometries. In addition to correcting for disjointed and overlapping components, we demonstrate hardware-specific corrections, differentiably optimizing the geometry of components to enable robot screwdriving for 86.7% of 60 novel natural language inputs, significantly outperforming prior work by a factor of ten. For ten of the structures, we physically demonstrate assemblability with two UR5e robots. This work marks a meaningful step toward on-demand robotic manufacturing, enabling the rapid production of customized, low-volume goods.

This work is devoted to a theoretical study of the interaction of a quantum three-level ladder system with a continuous electromagnetic field in a one-dimensional open waveguide. We consider a situation closely resembling stimulated emission - the scattering of a single-photon exponential pulse by an excited three-level emitter. Using the real-space formalism, we obtain an analytical expression for the wavefunction of our system. We show that, for the low anharmonicity of a three-level system inherent to a transmon (the most common type of artificial atom), the influence of the third level can have a significant effect on the system's behavior. Namely, the presence of the third level largely suppresses the stimulated emission effect if the relative anharmonicity is lower than $| \alpha_r | < 4\%$. However, for a three-level system, it is possible to obtain correlation effects such as photon bunching in the reflected field, which can also be 'switched off' by tuning the incident photon parameters.