Papers

The detection of high-energy astrophysical neutrinos has opened a new avenue for identifying cosmic particle accelerators. Blazars, active galactic nuclei (AGN) with relativistic jets oriented close to the observer's line of sight, are promising sites of hadronic interactions capable of producing PeV-scale neutrinos. We investigate the flat-spectrum radio quasar (FSRQ) PKS~0215+015 ($z \simeq 1.715$), positionally consistent with the IceCube-220225A neutrino event of estimated energy $\sim$154~TeV. We combine Fermi-LAT $\gamma$-ray data with Swift-XRT and Swift-UVOT observations to characterise the source around the neutrino epoch. PKS~0215+015 exhibited pronounced $\gamma$-ray, X-ray and optical activity in early 2022, consistent with a disturbance propagating along the jet. We construct broadband spectral energy distributions (SEDs) for the flaring interval and model them using leptonic and lepto-hadronic frameworks. The SED is well reproduced by a leptonic model comprising synchrotron, synchrotron self-Compton and external Compton emission, indicating that electron processes dominate. A co-accelerated proton population remains radiatively subdominant but requires a proton kinetic luminosity roughly two orders of magnitude above equipartition with the magnetic field. The predicted neutrino flux is well below that implied by a single IceCube-220225A-like detection. Independent analysis of short-term $\gamma$-ray variability yields an emission-region size consistent with the SED fit, supporting the model's physical self-consistency. We discuss the temporal and energetic plausibility of the association between PKS~0215+015 and IceCube-220225A and implications for future multimessenger studies of high-redshift FSRQs.

Robot manipulators are monitored by constraint-specific indicators whose units and gradient scales are not comparable, so they do not provide a common measure of the configuration-space motion remaining before violation. We define the feasibility distance field (FDF) as the distance, under a fixed positive-definite joint-space metric, to the union of infeasible configuration sets. Classical distance-to-set theory gives 1-Lipschitz continuity, almost-everywhere differentiability, and unit dual-gradient norm wherever the nearest projection is unique. The robotics contribution is an admissibility analysis showing when practical constraints define non-empty closed sets. We derive admissible formulations for external and self-collision, joint limits, dexterity, Cartesian and task-projected compliance, joint torque under payload, and dynamic manipulability. Since every field uses the same metric, heterogeneous constraints compose by a pointwise minimum, conditioned constraints retain a fixed distance space, and multi-robot constraints produce block-sparse gradients that identify which robots must react. We generate projection-based labels and train neural approximations with a distance loss and an Eikonal penalty. Simulations on a UR5e and a dual-arm cell evaluate seven fields using value, projection, sign, gradient, composition, and moving-obstacle diagnostics. Across 8,000 configurations, the largest feasible-side secant ratio is 0.920, mean learned gradient norms range from 0.994 to 0.998, and projection residuals range from 0.011 to 0.034 rad. Across 24 random obstacle paths, the external and composed collision fields achieve 90.4% and 91.6% success within 3 cm, with sign-error rates below 2%. The results support a common configuration-space margin and identify approximation errors near medial axes and sparsely sampled boundaries.

Autonomous parking in nonconvex and narrow environments remains challenging. Although optimal-control methods can explicitly enforce vehicle dynamics and collision constraints, nonconvexity compromises solver robustness and can cause failures. Large language models (LLMs) exhibit strong semantic reasoning capabilities, but directly generating dense trajectories makes it difficult to guarantee physical feasibility. We introduce SE-LLM-OCP, a unified framework in which LLMs make high-level discrete maneuver decisions, while an optimal-control module enforces low-level vehicle dynamics and collision constraints. Online, the LLM proposes sparse maneuver plans, decomposing the parking task into a sequence of short-horizon trajectory-optimization problems. A low-level solver then sequentially solves optimal-control problems. If the solver fails, the LLM aggregates failure evidence from the solver and validation stages to guide replanning. Offline, SE-LLM-OCP automatically evolves a structured decision-making knowledge base from scratch, driven by accumulated online failures. We validate our proposed framework in simulation on a car-like vehicle model and on a differential-drive robot. Our experimental results show that SE-LLM-OCP enables safer autonomous parking in narrow scenarios and demonstrates transfer of the same maneuver representation to a different kinematic platform.

We compare H2 high ro-vibrational observations of 5 PDRs (S140, IC63, Horsehead Nebula, NGC 2023 and Orion Bar) obtained with the IGRINS spectrograph to PDR models produced with the Meudon PDR code, in order to estimate the physical conditions and to constrain the physical and chemical processes that govern PDRs. We use newly flux-calibrated and extinction-corrected IGRINS H2 observations covering the 1.45-2.45 um range at a resolution of 45000, and adjust Meudon PDR models using both a simple chi2 minimization approach and a robust method using Bayesian inversion followed by posterior exploration via an advanced MCMC technique. The PDR models use specific incident FUV spectra for each PDRs based on theoretical stellar spectra from the Pollux database. The Meudon PDR code is able to reproduce more than 85% of the observed H2 ro-vibrational line intensities within a factor of two. We find that (1) a realistic modeling of the incident FUV field (both in term of geometry and of spectral shape) and (2) the inclusion of recent data on collisional de-excitation rates for high vibrational levels of H2 are key to this success. H2 ro-vibrational emission lines are found to provide good constraints on both the thermal pressure and the incident FUV field strength, G0, although with a non-negligible remaining degeneracy in most PDRs. Additional constraints, such as the spatial scales of the PDR derived from ALMA or JWST observations, are found to be able to lift this degeneracy. For low excitation PDRs, the observations provide evidence that nascent H2 molecules formed on grains have relatively low rotational energy and high vibrational energy, as predicted by theoretical and experimental studies of the surface formation of H2.

A/B testing requires large sample sizes, long timelines, and significant costs. When auxiliary predictions of experimental outcomes are available from machine learning models, uncertain prediction quality precludes replacing human experiments entirely, yet these predictions may still contain useful signal. We propose a principled framework for learning-augmented hypothesis testing that leverages predictions of unknown quality to reduce sample sizes while maintaining statistical validity. Predictions naturally vary in granularity, from coarse aggregate signals to fine-grained individual-level estimates, and our framework addresses both ends of this spectrum: (1) for population-level directional predictions, where only a binary signal on the treatment effect sign is available, we use an asymmetric test and prove consistency and robustness bounds within the learning-augmented algorithms paradigm; (2) for individual-level predictions, we introduce Generalized PPI++ (GPPI), extending Prediction-Powered Inference to handle nonlinear prediction errors through higher-dimensional transformations. Both methods benefit from accurate predictions while remaining robust to inaccurate or adversarial ones. We validate our framework using persona-based LLM simulations, where AI agents equipped with user personas predict individual behavior, as a natural prediction source spanning both granularity levels. Experiments on four real-world datasets demonstrate that our methods, combined with persona-based predictions, substantially reduce experimental costs while preserving rigorous statistical validity.

The High-Luminosity LHC (HL-LHC) will demand order-of-magnitude gains in analysis throughput, and increasingly those gains must come from GPUs that are not made by a single vendor. Leadership-class systems such as El Capitan, Frontier and LUMI are built on AMD accelerators, yet the Scikit-HEP analysis stack—and Awkward Array in particular—has grown up CUDA-first. We report on $rawkward$, a Rust-backed kernel engine that adds a ROCm/HIP backend for Awkward Array's nested, jagged, variable-length data structures. Our central finding is that a naive source-level port of CUDA kernels to HIP loses $5$–$10\times$ in performance on irregular kernels, because AMD's $64$-lane wavefronts, higher register pressure and more expensive divergence behave fundamentally differently from NVIDIA's $32$-thread warps. We show that a small, reusable set of optimization patterns—loop flattening, $128$-bit vectorized loads, splitting fused kernels, and profile-guided launch configuration—recovers CUDA-class performance without changing the public API. A Rust macro-and-match dispatch layer keeps a single, backend-agnostic call site while emitting vendor-specific kernel strategies, and the type system enforces buffer-size and lifetime correctness at compile time. On a two-socket AMD Instinct MI210 node we measure GPU speedups from $1.03\times$ (bandwidth-bound $sum$) up to $12.5\times$ ($count$) over $128$ EPYC~7763 CPU cores, and the Rust CPU kernels match or beat on aggregate the incumbent C++ kernels (geometric-mean runtime ratio $0.37\times$ across twelve kernels). We argue that these patterns constitute a practical recipe for performance-portable, vendor-agnostic HEP analysis kernels.

Multi-organ segmentation using deep learning requires large amounts of annotated patient data; however, institutions often lack sufficiently large and diverse annotated datasets. Privacy constraints further prevent institutions from sharing patient data to overcome this limitation. Moreover, due to the labor-intensive nature of annotation and the scarcity of diverse expertise, institutions typically have labels for only a small portion of their local data, leaving the larger unlabeled portion unused. In this work, we propose a flexible semi-supervised federated multi-task student-teacher framework that leverages federated learning (FL) to improve multi-organ segmentation using both labeled and unlabeled data across participating sites. At each communication round, the proposed framework initiates local training, where clients with labels for the same task form a federation to produce an aggregated teacher model. The resulting teachers generate task-specific features for all data at each client. Subsequently, all clients form a second federation to train a multi-task student model with a shared encoder and task-specific decoders that replicate the teacher-generated features across all segmentation tasks. The aggregated student model is then used to update the local teachers and initiate the next training round. Extensive experiments demonstrated the effectiveness of the proposed method compared with local and federated single-organ models, yielding an average performance gain of 13 percent across clients. The experiments also demonstrated the impact of multi-task learning and unlabeled data and the applicability of the framework in relaxing labeled-data requirements for client participation. The code is available at https://github.com/AshknMrd/FedMust.

Latent world models learn predictive representations for autonomous driving, but the relational semantics these states preserve often remain implicit. We investigate whether traffic scene graphs can serve as privileged semantic supervision for latent world representations. Building on LAW, we construct actor-centric scene graphs from nuScenes 3D annotations, encode their serialized relational structure using a frozen text embedding model, and align the visual latent representations with this semantic target during training. We remove the supervision branch at inference, so it requires neither scene graphs nor 3D annotations and adds no test-time computation. On nuScenes, our method reduces average trajectory L2 error from 0.661 to 0.622 (5.9%) and collision rate from 0.456 to 0.217 (52.4%) relative to our retrained LAW baseline. It also outperforms an unstructured caption-style semantic target, supporting the benefit of explicit relational structure for latent world-model representation learning.

How should natural language processing models be selected and adapted for global health literature in environments where annotated data and computational resources are limited? This thesis investigates these challenges through experiments on semantic tag discovery, named entity recognition (NER), and multi-label topic classification. First, skip-gram word2vec models trained on progressively larger specialized corpora are compared with BioWordVec to assess how corpus size and domain context influence tag discovery. Vocabulary coverage and qualitative evaluation indicate that broader coverage does not necessarily yield more useful domain-specific associations. The analysis then turns to entity extraction, comparing convolutional spaCy models with a RoBERTa-based transformer on 1,000 annotated sentences. Under a lenient scoring protocol, the transformer achieves 0.80 micro-F1 versus 0.65-0.69 for convolutional models, but takes 82 seconds rather than 5-6 seconds. This trade-off motivates fine-tuning convolutional models and integrating a disease recognizer that achieves 81.33% test F1 on the NCBI Disease Corpus. Combined with PDF preprocessing, entity filtering, and MeSH enrichment, the resulting pipeline supports document-level indexing. To complement entity extraction with thematic annotation, MiniLM-based few-shot classification is compared with BART-MNLI zero-shot inference across 50 topics and 1,000 handcrafted test sentences. BART-MNLI achieves 95.2% single-label accuracy versus 59%; reported multi-label accuracies are 88% and 32% under partly manual assessment. However, its higher inference cost limits practical integration. The results show where domain specialization and lightweight adaptation offer practical value, and where transformer accuracy justifies higher inference costs, providing an empirical basis for building knowledge systems under resource constraints.

In the vertex cover interdiction problem, we are given an undirected graph $G=(V,E)$, two integers $t$ and $k$ and a vertex subset $B\subseteq V$, and we are asked to find a set $X \subseteq B$ with $|X|\leq t$ such that $X$ hits (i.e., intersects) all the vertex covers of $G$ of size at most $k$. Recently, Grüne and Wulf proved that the problem is $\Sigma_2^p$-complete. However, their reduction relied on the fact that the vertex cover problem is NP-complete. This, in turn, means that we do not know the complexity status of the vertex cover interdiction problem when the input graph is restricted to a bipartite graph since the vertex cover problem can be solved in polynomial time for bipartite graphs. One of our main results shows that the vertex cover interdiction problem is NP-complete for bipartite graphs. In contrast, when $k$ is restricted to the minimum vertex cover size, i.e., we are only required to hit all the minimum vertex covers, we show that the vertex cover interdiction problem can be solved in polynomial time for bipartite graphs. This motivates us to study the parameterized complexity of the vertex cover interdiction problem for bipartite graphs when the difference of $k$ and the minimum vertex cover size is taken as a parameter. With this parameter, we show that the problem is $\mathrm{W}[1]$-hard, but can be solved in polynomial time when the parameter is constant (i.e., in XP time). We also show that the problem is fixed-parameter tractable when parameterized by $k$.

We consider the parametrised family of sets $$ E(x,y)=\left\{\sum_{n=1}^{\infty}\frac{\varepsilon_n}{4^n}: (\varepsilon_n) \in \{0,x,y,x+y\}^{\mathbb{N}}\right\} $$ for $(x,y) \in \mathbb{N}^2$. This family can be viewed through three lenses: (a) as homogeneous self-similar sets; (b) as achievement sets of bi-geometric series; or (c) as the set of `rational' orthogonal projections of the four-corner Cantor set. We synthesise these three perspectives to obtain a complete topological classification of $E(x,y)$ for $(x,y) \in \mathbb{N}^2$. Next, we collapse this topological classification to a binary one according to whether or not $E(x,y)$ has interior. When this binary classification is visualised, it reveals a two-colour tiling $T$ of the lattice $\mathbb N^2$, which, despite being visibly structured, turns out to be aperiodic; indeed, we prove it has no non-trivial translational symmetries. Due to the rigidity of our model, this same binary classification simultaneously captures several dichotomies. Most notably, when the family $\{E(x,y)\}_{(x,y) \in \mathbb{N}^2}$ is viewed through the theory of self-similar sets, $T$ can be seen to describe the emergence of dimension drop within the family. Finally we examine the mechanism underlying the tiling's aperiodic order. By considering the number-theoretic properties of the tiling, we characterise its substitution structure, and discover that $T$ is a factor of a substitution tiling on four “hidden” arithmetically defined states.

We establish arbitrary-order a priori regularity estimates for the reverse heat flow in the Ornstein–Uhlenbeck setting, that is, for the probability-flow ODE of score-based diffusion models. For compactly supported, possibly singular targets satisfying a dimension-uniform doubling condition on supporting-cap masses, we bound the iterated material derivatives of the flow and their first spatial derivatives pointwise, with constants independent of the dimension $d$ and explicit in time and support radius. The proof rests on two ingredients: a spatially uniform bound on normal-direction posterior fluctuations, which is the only point where the geometry of the target enters, and a centered posterior-moment normal form closed under material differentiation. This algebraic structure, together with a weighted regularity calculus, yields quantitative bounds at every order, including the mixed space–time directional derivatives required by Runge–Kutta stages. As an application, for exact-score sampling stopped at forward time $\delta>0$, order-$p$ Taylor and explicit Runge–Kutta schemes reach accuracy $\varepsilon$ in $\widetilde O(d^{1/p}\varepsilon^{-1/p})$ steps in total variation, and the Taylor scheme in $\widetilde O(d^{1/(2p)}\varepsilon^{-1/p})$ steps in $W_2$.

Tactile sensing is increasingly being incorporated into learning-based robotic manipulation, yet many existing approaches rely on spatially distributed sensors. Here we introduce {SpectRobot}, a framework that transforms single-point tactile signals into compact time-frequency spectrograms. These spectrograms encode high-bandwidth tactile histories as fixed-size image-like representations. They can be processed by standard vision encoders and integrated into learning pipelines originally developed for vision, while preserving temporal and frequency information unavailable to conventional cameras. Rather than increasing spatial density through arrays of tactile elements, SpectRobot exploits the rich dynamics contained in sparse, high-bandwidth single-point measurements. In our implementation, the sensors are mounted away from the contact surface while remaining mechanically coupled to it, reducing direct exposure to wear and potentially improving robustness in harsh environments and for long-term deployment on dexterous robots. Our experiments demonstrate that: (1) a robot can exploit single-point vibration signals to solve a visually occluded manipulation task; (2) temporal history strongly influences policy performance, while sensing bandwidth controls the spectral information available, with measurements extending to 100~kHz; and (3) the same representation can be used across different tactile sensing technologies mediated by acceleration, force, or strain. We further show that capabilities previously associated with research-grade instrumentation can be accessed using readily available, off-the-shelf hardware. We believe that broader access to high-bandwidth tactile sensing could facilitate the integration of contact dynamics into embodied learning systems and, for some tasks, offer an alternative or complement to increasing the spatial density of tactile sensing.

Answering epidemiological questions from real-world clinical data requires medical coding, schema-aware SQL, and validation of implicit choices about populations, denominators, and time. We present Ascent, an agentic system that exposes medical coding, question answering, and cohort analysis through a shared Model Context Protocol tool surface for standardized and native schemas. We introduce EpiTrap, a dataset testing whether systems avoid recognized pharmacoepidemiological errors, and compare a fixed pipeline with agents across models and orchestrators. With capable models, agents improve accuracy over the fixed pipeline by an average of 27 and 20 percentage points on native and standardized schemas, respectively. These gains require more tool calls and longer runtimes. Experience from real projects highlights the system's value for feasibility assessment, diagnostic iteration, and expert-guided analysis.

The proposed pipeline integrates a representation-flow convolutional neural network with a dynamics- and uncertainty-aware tree-based Gaussian Process classifier. In this framework, latent motion dynamics are exploited both as discriminative representations and as a source of input uncertainty, enhancing robustness against temporal variations and abnormal motion transitions. Compared with conventional deep learning approaches, the proposed strategy requires less training data and offers improved computational efficiency. To further improve classification performance, we introduce novel semantic-aware compound kernels that effectively capture semantic, flow, and dynamic information embedded in surgical video features. In addition, uncertainty-aware kernels are developed to strengthen the robustness and practical applicability of the compound kernel framework. The proposed method is evaluated on two benchmark datasets, namely the JIGSAWS and the Cataract-LMM (Capsulorhexis) datasets. Experimental results demonstrate strong performance across both datasets, including the LOSO and LOUO evaluation protocols on JIGSAWS, including the subject-independent LOUO protocol on JIGSAWS, on which the framework attains a mean accuracy of \ph{96.9}%; results under the within-subject LOSO protocol are reported for comparability with prior work, achieving competitive accuracy while substantially reducing computational cost. Overall, the proposed pipeline provides an efficient and accurate framework for video-based surgical skill assessment.

We study strict ground-level gaps for autonomous nonlinear Dirac equations on noncompact metric graphs. The relevant level at infinity is the autonomous full-line level \(d_\lambda^\infty=d_{\lambda,\mathbb R}\), since a concentrating sequence escaping along a half-line sees the real line after recentering far from all vertices. We prove that, uniformly for \(\lambda\) in a compact subinterval \(I\Subset(-mc^2,mc^2)\), the presence of a sufficiently long pendant path in the essential reduction of the graph implies \[ d_\lambda(\mathcal G)<d_\lambda^\infty. \] The proof uses a half-line restriction of a symmetric full-line ground state, uniform exponential decay, resolvent localization for massive Dirac-Kirchhoff spectral projections, and a compactness argument for generalized Nehari fibres. We also identify elementary graph classes for which no such gap can hold: pure transmission graphs whose essential reduction is isometric to the full line satisfy \(d_\lambda(\mathcal G)=d_\lambda^\infty\).

Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form $\mathcal{L}(t)=\alpha(t)A+\beta(t)B$, when the commutator $[A,B]$ is a simultaneous eigenoperator of the adjoint actions of $A$ and $B$, namely $[A,[A,B]]=\lambda_{A}[A,B]$ and $[B,[A,B]]=\lambda_{B}[A,B]$. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.

AI coding interfaces present generated code either all at once or token-by-token. These rendering strategies reflect model generation rather than how programmers actually read code: selectively, non-linearly, and guided by the structure. We argue that code rendering is a first-class interaction primitive that shapes how programmers read and understand code. To explore this design space, we introduce structured rendering, a technique that reveals code in semantically meaningful chunks derived from its syntactic hierarchy, exposing high-level structure before low-level details. To isolate rendering effects on visual attention, we conducted an eye-tracking study with 53 participants comparing static, character-based, and structured rendering. Our findings show that rendering alters visual attention and reading behavior: dynamic rendering induces fewer but longer fixations and more sustained focus, while structured rendering further guides attention toward semantically meaningful units and supports high-level understanding. We release the anonymized dataset with an interactive demo (https://codegaze.vercel.app/) to support future research.

Seismic feature extraction and acoustic impedance inversion are important for subsurface characterisation, but sparse well-log data limit the generalisation of data-driven inversion models across different areas. Self-supervised masked pretraining offers a way to exploit large volumes of unlabelled seismic data; however, conventional approaches often overlook the directional characteristics of 3D seismic data. We propose a direction-aware masked autoencoder (DA-MAE) that distinguishes lateral reflector structure from vertical waveform characteristics in 3D post-stack data. The framework incorporates this distinction into token representation, masking geometry, and reconstruction constraints on reflector continuity and waveform fidelity. We evaluate DA-MAE through masked reconstruction on an independent field survey and cross-area acoustic impedance inversion using two additional field areas. Reconstruction experiments show that performance is more sensitive to lateral token resolution than to moderate changes in vertical patch length, and that increasing encoder capacity does not fully compensate for coarse tokenization. Moreover, the preferred token scales and masking strategies vary between reconstruction and inversion, suggesting that reconstruction fidelity alone is not a reliable indicator of transferability. In cross-area inversion, the pretrained representations remain effective in the target area and improve impedance prediction, demonstrating their transferability across different seismic surveys. These results provide practical guidance for seismic-specific masked pretraining and its application to acoustic impedance inversion.

Let $\varphi\in L^\infty(\D)$. We study compactness criteria for \(T_\varphi\) on the Bergman space $A^2(\D)$. Axler and Zheng~\cite{AZ1998} established a necessary and sufficient condition for compactness in terms of the Berezin transform. For a general bounded measurable function $\varphi$, however, its Berezin transform $\tilde{\varphi}$ does not readily reveal the intrinsic properties of $\varphi$. Motivated by a characterization in terms of the symbol itself, Zhu~\cite{ZhuSlides} proposed a conjecture on compact Toeplitz operators. In this paper, we characterize compactness of $T_\varphi$ on the unweighted Bergman space in terms of local averages of the symbol. We prove that compactness is equivalent to the vanishing of averages over Bergman disks of any prescribed fixed radius. We also establish an equivalent criterion in terms of Carleson box averages that tend to zero uniformly in the angular variable. Finally, we construct a nonnegative bounded symbol whose Carleson box averages tend to zero at every fixed angle, although the associated Toeplitz operator is not compact.

Prior case retrieval (PCR) aims to identify precedent cases relevant to a given query case. Existing PCR benchmarks and methods predominantly operate at the document level, treating entire judgments as the unit of relevance. This formulation is suboptimal for legal practitioners, as judgments address multiple legal issues and only a small subset of paragraphs is relevant to a particular query. Addressing this gap, we introduce UK-PRBench, a benchmark for paragraph-level precedent retrieval in UK case law, constructed from judgments obtained from the UK National Archives and covering a broad range of UK courts and tribunals. Furthermore, we evaluate state-of-the-art retrieval models and establish baseline results. Our experiments show that paragraph-level precedent retrieval remains challenging for current retrieval approaches, highlighting substantial room for improvement. UK-PRBench provides a standardised benchmark for evaluating fine-grained precedent retrieval and advancing retrieval systems for the UK legal domain.

Model merging aims to consolidate multiple task-specific models without access to extra training process. However, existing subspace-based methods largely rely on a uniform treatment of task updates, overlooking their intrinsic spectral and depth-wise heterogeneity. We identify two key deviations from this assumption: different tasks require different subspace capacity and exhibit different tolerance to spectral transformation, while subspace projection introduces depth-dependent distortion. Based on these observations, we propose SADA-Merging, a spectrum-aware and depth-adaptive framework for data-free model merging. SADA-Merging allocates task-specific subspace capacity according to spectral complexity, adapts spectral preservation according to task-wise plasticity, and applies depth-dependent anchoring to compensate for projection-induced distortion. This enables the fusion process to adapt to both the intrinsic geometry of each task and its sensitivity across network depth. SADA-Merging operates directly on task updates and is applicable to both full fine-tuning and LoRA settings. Extensive experiments demonstrate consistent improvements over existing data-free merging methods across different task scales and adaptation settings.

Programmable photonic circuits have emerged as a promising platform for applications ranging from optical communications to artificial-intelligence computing and quantum information processing, but their scaling is fundamentally constrained by their essential building block, the optical phase shifter. Existing phase-shifter technologies face inherent trade-offs among power consumption, operating speed, modulation efficiency, optical loss, and thermal crosstalk, making it challenging to realize high-performance, large-scale programmable photonic circuits. Here, we present a programmable photonic circuit based on InGaAsP/Si hybrid metal-oxide-semiconductor (MOS) phase shifters that combines ultralow power consumption, high-speed operation, high modulation efficiency, low optical loss and negligible thermal crosstalk. The phase shifters combine the low leakage current of a MOS capacitor with the strong carrier-induced refractive-index modulation of an InGaAsP membrane, achieving a static power consumption below 30 fW/$\pi$, a switching time of 555 ps, a phase-modulation efficiency ($V_\pi L$) of 0.13 Vcm and a carrier-induced excess insertion loss of only 0.20 dB/$\pi$. We integrate these phase shifters into a programmable Mach-Zehnder interferometer mesh and demonstrate optical switching and programmable unitary transformations, while maintaining femtowatt-level static power consumption across integrated phase shifters. We further demonstrate circuit-level operation with negligible thermal crosstalk, addressing a major obstacle to densely integrated programmable photonic circuits. These results establish a foundation for scalable, high-performance programmable photonic systems for next-generation signal processing and computation.

We prove that every proper subdomain of the Euclidean space equipped with its quasihyperbolic metric is CAT(2). The CAT property leads to a positive resolution of Väisälä's uniqueness, prolongation, quasihyperbolic convexity, and local geodesic conjectures on quasihyperbolic geodesics affirmatively on all dimensions, extending the two-dimensional results by Herron. The sectional curvature bound is optimal as demonstrated by the complement of two points in dimensions at least three. We also show that in any quasihyperbolic domain, quasihyperbolic spheres up to radius $\pi/\sqrt{2}$ are $\mathcal{C}^{1,\frac{1}{2}}$-diffeomorphic to the Euclidean sphere. Consequently, we answer a question by Gehring and Vuorinen on the regularity of such spheres. Similar techniques lead to a positive resolution of Väisälä's conjecture on the Euclidean convexity of quasihyperbolic balls up to radius $\arctan(\sqrt{2})/\sqrt{2}$. We establish that in all dimensions, the quasihyperbolic metric is CAT(0) on convex domains. This leads to a positive answer to a question by Martio and Väisälä on the quasihyperbolic convexity of quasihyperbolic balls on such domains. Finally, we prove that a variable Alexandrov curvature lower bound for a quasihyperbolic domain self-improves to a global lower bound of $-1$ and is equivalent to the concavity of the domain.

Electricity forecasting often involves spatially related signals observed over regions, substations, and feeders, and Graph Neural Networks (GNNs) represent these relations through a graph. Building a complete GNN forecasting experiment is nonetheless laborious, because graph construction, model selection, training, aggregation, and interpretation often require separate tools. We present GraphToolbox, an open-source Python framework that unifies these stages in one configuration-driven pipeline built on PyTorch Geometric. It offers data-driven graph construction, a single interface for most graph convolution operators of PyTorch Geometric and for recurrent graph cells, online expert aggregation, forecasting interpretability, and significance testing on forecasts. We use GraphToolbox to run a controlled benchmark: we compare architectural and modeling choices for French electricity load and net-load forecasting at regional and national levels under a common experimental protocol. On load, most evaluated graph convolutions outperform additive, recurrent, and foundation-model baselines. Pooled XGBoost, trained on the same inputs, has a lower RMSE than the best graph models, although the difference is not significant. Online expert aggregation and daily model updates improve accuracy further. On net-load, graph models outperform additive, recurrent, and XGBoost baselines, with further gains from forecasting the physical components separately. Statistical tests do not identify a single best convolution for load forecasting.

Multi-period Repetitive Control (MPRC) can lead to amplification at non-repetitive frequencies due to the multiplication of multi-period repetitive control in their closed-loop sensitivity functions, which leads to closed-to imaginary poles. We propose a MPRC structure that eliminates such interaction. The scheme can be equivalently converted into a disturbance observer to improve robustness to frequency uncertainties. We derive an upper bound on the sensitivity function that can be optimized at either repetitive or non-repetitive frequencies. Experimental results on an active vibration isolation system show superior performance over existing robust MPRC schemes, and the capability to suppress unknown time-varying periodic disturbances.

New theoretical model of the dynamic current-voltage characteristics anomalies in HTc superconductors in slowly varying magnetic field has been proposed. The model is based on an analysis in details of the magnetic flux penetration into HTc superconducting slab in such case. The comparison of model with previous experimental data has been presented. Theoretical analysis resulting from a new solution of diffusion equation is given as well as other one based on phenomenological critical state model.

Molecular properties govern how molecules interact with one another or external fields. Accurate molecular properties are essential for constructing intermolecular interaction models, and to achieve high accuracy we need to go beyond leading-order (dipolar) terms. This work presents CCSD(T) references for 73 small non-spin-polarized molecules for molecular dipole and quadrupole moments, and dipole-dipole and quadrupole-quadrupole polarizabilities. Using these results, we provide a holistic performance analysis of molecular properties computed with HF, MP2, CCSD, and a wide range of density-functional methods. Additionally, we investigate in detail what levels of basis sets are required to simultaneously describe all properties in the data set. The best-performing density functionals for all four properties are the asymptotically cor- rected hybrid GGAs B97-3-AC, closely followed by PBE0-AC. Surprisingly, modern meta- GGAs and range-separated functionals perform inconsistently, with large errors in the quadrupo- lar properties. These results have direct implications for methods for intermolecular interac- tions, such as symmetry-adapted perturbation theory based on density functional theory, or for the quality of properties and interactions in machine-learning datasets. Finally, for DFT methods, the Jensen aug-pcseg-2 basis set is a computationally efficient alternative to more established basis sets, but for generating correlated references, third-row elements benefit from core polarization, and double augmentation is strictly necessary for quadrupole-quadrupole polarizabilities.

Problem definition: We study dynamic pricing of substitutable products with finite, product-specific inventories. Customer substitution couples pricing decisions across products, while the inventory state makes exact dynamic programming intractable at realistic scale. Methodology / results: We develop two MNL-guided policy-learning approaches that replace the dynamic program with a statistical mapping from inventory states to pricing decisions. The first learns prices directly, while the second learns inventory opportunity costs and converts them into prices using the optimal MNL pricing rule. Both policies are trained using decision-focused learning. We also propose an efficient method to generate anticipative customer-choice targets to train our policies. Managerial implications: We conduct an extensive numerical evaluation of our approaches. On small instances for which the optimal dynamic program can be computed, the learned policies achieve average optimality gaps below 0.4%. On larger airline-motivated instances, they consistently improve on the tested revenue-management benchmarks. The comparison between the two architectures also highlights the role of model structure: using the MNL pricing characterization is particularly effective when demand is well described by MNL, while directly learning prices provides greater flexibility under heterogeneous mixed-MNL demand.

The Lean proof assistant has a rich library of mathematical formalizations that are interesting to users of other proof assistants. To help with the translation of this library to other systems, we present a theory in the Dedukti logical framework in which one can encode Lean terms and types, and define a typability-preserving translation from some large subset of Lean to that Dedukti theory.