Papers

Leave-one-out (LOO) cross-validation, a standard tool for Bayesian model assessment, evaluates each observation using a LOO predictive distribution derived from the model itself. In this work, we introduce an alternative construction in which posterior predictive simulation connects the Bayesian model to an external pretrained predictive learner. Our method, Predictive-Context LOO (PC-LOO), fits a Bayesian model once, generates posterior-predictive synthetic data, and uses them as context for the learner to approximate each LOO predictive density. Under an oracle construction, averaging contexts generated from the LOO posterior recovers the exact LOO predictive density. Practical PC-LOO replaces the oracle predictor by the pretrained learner and the LOO posterior by the full posterior. We quantify these errors through learner compatibility $C_i$ and deletion influence $V_i$, obtaining $H^2 (p^{LOO}_{i} , q^{PC}_{i}) \leq C_{i} + V_{i}$. The identity also holds for any fixed subset of $M$ context points, allowing $M \ll n - 1$ as the learner's context budget, and scalability to large datasets. Experiments with TabICL support this decomposition, deletion influence decays approximately as $n^{-1}$, while learner compatibility can remain limiting at large $n$. PC-LOO remains accurate with reduced context sizes, while model comparison accuracy is governed by differences in approximation error across models rather than their absolute errors. More broadly, PC-LOO establishes posterior predictive simulation as a principled interface for integrating pretrained predictive learners into Bayesian workflows.

Strong light–matter interactions have attracted significant interest in physical chemistry due to the potential for modifying molecular processes by hybridizing with cavity photons and forming polaritonic states. However, for a disordered molecular ensemble within an optical cavity capable of supporting multiple photon modes, theoretical understanding of multimode polaritons remains incomplete, particularly regarding whether and how distinct photon modes are mutually coupled through molecules. In this work, we generalize the collective mode expansion formalism to incorporate multiple photonic modes and show that spatial and orientational disorder in the light–matter coupling strength (originating from dipole orientation fluctuations and photonic field inhomogeneity) can mediate cross-mode coupling. This disorder-induced coupling allows for energy transfer to otherwise unexcited photon modes through a mechanism termed disorder-induced multimode activation (DIMA). Using an effective one-dimensional Fabry–Pérot cavity as a test system, we demonstrate that the cross-mode energy transfer through DIMA can be controlled by changing the molecular layer thickness and the optical properties of the mirrors. Furthermore, we show that DIMA is robust against weak energetic disorder. This mechanistic understanding lays the foundation for a systematic control of multimode photon coupling using disorder-induced effects.

6G networks are expected to sense their surroundings using the same waveforms that carry data. We ask how much can be learned about the shape of an object from the terahertz echoes that user equipment transmissions produce as they scatter from that object on their way to a ceiling-mounted access point, with no sensing hardware beyond the communication link itself. We build a physics-based multistatic forward model at a 300 GHz carrier with 50 GHz of bandwidth, combining Physical Optics (PO) and Physical Theory of Diffraction (PTD) scattering with an image-source multipath lattice, molecular absorption and directional horn antennas. The model makes explicit a property of the PO mechanism hierarchy that is usually left implicit. Six physically distinct mechanisms share only three frequency exponents, so the spectral slope does not by itself determine which mechanisms a target presents and therefore cannot by itself determine its geometry. Angular diversity is accordingly a requirement for identifiability rather than an optional refinement. We compare a transmitter-count-invariant 2D-CNN with a physics-informed RBF-SVM on object orientations never seen in training. Accuracy climbs from roughly 70 percent with one transmitter to 96-97 percent with 20. The CNN gains in two regimes, irregular placement and lossy targets, while on metal under quasi-uniform placement the SVM baseline is fully competitive. Performance falls off gradually under occlusion, holding 78 percent with three quarters of the surface hidden and 63 percent when the classifier has never seen an occluded target. Multi-object scenes are limited by interference between overlapping returns rather than by angular coverage, so presence detection saturates after roughly four transmitters.

Quantum LDPC codes promise to reduce the overhead of fault-tolerant quantum computation, but their practical use requires efficient logical gates, measurements, and access to non-Clifford resources. Here, we develop a complete set of computational primitives for La-cross hypergraph product codes. For a subclass of these codes, we show that seed automorphisms together with fold-transversal gates generate the full logical Clifford group up to Pauli corrections. We further prove that every rank one logical operator admits $D$ pairwise disjoint physical representatives, enabling parallel gauging and a space–time tradeoff for logical measurements. Finally, we construct an addressable surface code interface for injecting externally prepared resource states into selected logical qubits. Together, these results establish La-cross codes as a simple, low-connectivity generalisation of surface code computation, retaining analogous computational primitives while providing a complete Clifford+$T$ instruction set across multiple encoded qubits.

Non-prehensile manipulation with mobile robots has primarily targeted placement in coarse goal regions. Precision placement has been studied with manipulators on benchmarks such as Push-T, where an omnidirectional end effector can readily re-approach an object from any side. For a mobile robot, correcting the same placement errors may require wide repositioning maneuvers around the object. We formalize multi-object pushing with a mobile robot as a multi-target assignment problem at tight tolerances. We propose a diffusion planner with a causal factorization: each robot denoising step is followed by an object step conditioned on the current clean robot estimate. This factorization allows us to sample multiple object outcomes for a single robot plan, capturing the multi-modality of pushing. We also design a set of pushing-specific costs for mobile robots, used for both guidance and best-of-$N$ sampling at inference. On Push-T, our planner attains the highest success rate of the methods we compare, while having the lowest rate of implausible object motion. Across three multi-box pushing environments resembling warehouse scenarios, it raises the fraction of boxes placed by $21.5$ percentage points over an unguided baseline, and replans $1.8\times$ faster than a planner that denoises the two trajectories together. Lastly, we deploy the guided planner on a TurtleBot 3 Burger with object shapes absent from the training data, where it places $85.0\%$ of objects within tolerance against Diffusion Policy's $37.5\%$.

Let \(X\) be a smooth connected complex projective variety with an effective algebraic \(\mathbb C^{\times}\)-action, a nonempty finite fixed locus whose weights are \(\pm1\). We show that if its Hattori line bundles are nef, then \(X\) is algebraically isomorphic to \((\mathbb{P}^1)^{\dim X}\), and these bundles become the hyperplane bundles of the factors. The product statement follows from the nef-complexity classification of Enwright and collaborators, and we describe the isomorphism through global sections. To test the required nefness we specialise the orbit-graph criterion of Romano and Wiśniewski. The Hirzebruch surface \(\mathbb F_2\) is an example why the topological hypotheses alone do not imply either the product conclusion or the Fano property.

The standard Yee finite-difference time-domain (FDTD) algorithm uses Maxwell's equations to replace first order temporal derivatives with spatial curls. In this work, the relation is extended to arbitrary orders: a Time-Space Theorem establishes the correspondence between higher-order temporal derivatives and successively higher-order spatial curl operators. Based on this relation, an arbitrary-order framework for electromagnetic field approximations is developed. The framework constructs higher temporal orders through higher curl orders and permits different spatial discretizations and curl-estimation techniques, thereby providing a general basis for developing numerical algorithms of arbitrary orders. As one implementation, an arbitrary-order FDTD algorithm is constructed using staggered time and space stepping together with recursive curl estimations. Numerical simulations of an initial-value problem are performed for temporal approximation orders from second to tenth order while the spatial and temporal step sizes are kept fixed. Comparisons with the analytical solution show that the errors decrease rapidly and monotonically with increasing approximation order. These results demonstrate the practical potential of the framework for high-accuracy electromagnetic computation and provide a basis for further development of arbitrary-order numerical methods.

We obtain the $L^3$ reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a preliminaries section. The proof passes from geometric concentration of packet coefficients to regularity of the analyzed wave, and then from free waves to arbitrary functions supported near the cone. As a consequence, we obtain the corresponding $L^3$ estimate for the sphere and elliptic paraboloids in three dimensions.

Background: Discontinuity in neonatal EEG is a critical marker of brain dysfunction but can be difficult to quantify visually. Inter-burst intervals (IBIs) are a key characteristic of discontinuity, yet their definition does not easily translate to AI detection. Objectives: To introduce low-voltage intervals (LVIs), defined exclusively by amplitude and duration, as a context-independent alternative to IBIs, develop an AI detection method for LVIs, and assess their clinical utility as a marker of brain injury. Methods: We developed a ConvNeXt model to detect LVIs and compared its performance with existing methods. We then tested the clinical relevance of detected LVIs across four applications: 1) grading background EEG abnormalities on an open benchmark dataset, 2) classifying clinical hypoxic-ischaemic encephalopathy (HIE) grades and comparing with a normal EEG dataset, 3) seizure prediction, and 4) association with seizure burden. Results: For training and validation, 654 hours of per-channel EEG from 123 neonates were reviewed and 51,162 LVIs were annotated. On held-out validation, ConvNeXt had an AUC of 0.996 and a Matthews correlation coefficient of 0.926. Model-reader agreement exceeded inter-reader agreement ($\Delta \kappa = 0.025$, 95% CI: 0.007 to 0.045, $p<0.001$), attaining expert-level equivalence. On a combined dataset of 444 neonates, percentage LVI showed a strong association with EEG grades (Spearman's $\rho=0.801$), a moderate association with HIE grades ($\rho=0.384$), a weaker association with seizure burden ($\rho=0.244$), and a strong seizure prediction capacity (AUC $=0.872$). Conclusion: AI detection of LVIs achieves expert-level equivalence, whereas quantitative features do not. Automated LVI quantification provides a robust clinical biomarker of neonatal encephalopathy associated with background EEG activity, HIE severity, and seizure risk.

Efficient sampling from Bayesian posterior distributions in high dimensions remains a hard problem, despite advances in theory and algorithms. Multiple steps are usually required to draw unbiased samples, for example, iterations of an MCMC algorithm or integration steps in a diffusion-based amortised sampler. However, scalable one-step amortised inference remains a challenging open problem. In this work, we build upon recent progress in data-driven generative modelling to offer a possible solution for one-step amortised sampling. Our one-step implicit sampler (OSIS) uses short-time MCMC dynamics to define a local target for the evolution of an implicitly modelled distribution. In the asymptotic limit, the modelled distribution is a fixed point of the MCMC kernel and thus samples from the target. We analyse the convergence properties of OSIS and show connections with other generative modelling and sampling algorithms. We study various design choices and show that OSIS performs well compared to multi-step amortised samplers and non-amortised MCMC baselines while being far more efficient at sampling time.

We study products of independent, identically distributed random matrices with an exponential moment and a simple top Lyapunov exponent, without assuming irreducibility. Outside an exceptional invariant subspace called the equator, we establish contraction on average for a weighted projective distance and a spectral gap for the associated Markov operator. We obtain a central limit theorem, a Berry–Esseen bound, deviation estimates near the mean, and an almost sure invariance principle both for the growth of a fixed vector outside the equator and for the operator norm. For fixed vectors, a non-arithmeticity assumption also yields a local limit theorem and a renewal theorem. Our contraction criterion applies more generally to mostly contracting random maps on locally compact spaces with a Lyapunov function, including certain random interval maps.

Low-density transiting gas giant exoplanets are key benchmarks for atmospheric studies. Despite their large-scale heights, many of them remain poorly characterised. We present the first atmospheric investigation at high-resolution of the inflated (R$_\mathrm{p}$$\sim$1.4 R$_{\mathrm{J}}$), hot Jupiter (T$\sim$1500$ \mathrm{K}$) WASP-13 b aiming at constraining its atmospheric composition and refine its orbital geometry. We analysed four transits observed with GIARPS at the TNG. Updated stellar and planetary parameters were re-derived from the most precise literature values, and a new Rossiter-McLaughlin analysis was performed to measure the projected spin-orbit angle ($\lambda$) and stellar rotational velocity ($v\sin{i_\star}$). Atmospheric signals were searched using high-resolution spectroscopy, both with cross-correlation and single-line analyses, targeting key atomic and molecular species (e.g. \ion{He}{I}, H$\alpha$, \ion{Na}{I}, H$_2$O, CO). We find a well-aligned orbit ($\lambda$ = 2.7$\pm$1.1$^\circ$) and $v\sin{i_\star}$ = 4.5$\pm$0.1 km s$^{-1}$, improving upon previous constraints. No significant atmospheric absorption is detected in either VIS or NIR data. Injection-and-recovery tests exclude an isothermal atmosphere with metallicity [M/H]$\lesssim$10$\times$[M/H]$_\odot$ and simultaneously a grey cloud top pressure P$_{\rm cloud}\gtrsim10$ mbar, under the assumption of chemical equilibrium. WASP-13 b appears to belong to the class of low-density hot Jupiters with weak or featureless transmission spectra, most likely shaped by the presence of high-altitude clouds. Although a highly metal-enriched atmosphere cannot be fully excluded, current evidence disfavours this scenario. Further observations with next-generation facilities will be essential to characterise the atmospheric properties of this challenging target.

Wood-image benchmarks can yield optimistic estimates when images from the same tree occur in both training and test sets. WoodBR-Cross contains 4,875 transverse-surface images in 38 operational taxonomic classes, linked to 303 distinct trees identified by numeric catalogue witness codes (codigos-testemunho) in the Brazilian Forest Service collection. A species-level subset comprises 3,406 images, 20 classes and 214 trees. Three tasks compare duplicate-aware image partitions for all classes (A), image partitions for the species subset (B1), and individual-tree-disjoint partitions for that subset (B2). In B2, all images from each tree are kept together, so no tree is shared across training, validation or test within a fold. ResNet-50, ConvNeXt-Tiny and ViT-B/16 were evaluated with three outer folds, internal validation and five training seeds. Handcrafted and frozen-feature baselines complement border-only and randomized-label controls. Validation-selected ConvNeXt-Tiny achieved B2 tree-level macro-F1 of 0.8621 +/- 0.0317; frozen DINOv2 features yielded 0.9000 +/- 0.0722. Values are means and standard deviations across three seed-averaged fold means. Results estimate performance on previously unseen trees from this collection.

In characteristic zero, we prove that the Tor algebras of the generic, symmetric, and skew-symmetric determinantal rings are Koszul with respect to a natural regrading. In particular, their Eilenberg–Moore spectral sequence degenerates, which allows us to explicitly determine the Poincaré series of their residue fields and answers a problem raised by Avramov. To do this, we construct the universal hook algebra and prove that it has a quadratic Gröbner basis and thus is Koszul. This leads to a new standard monomial construction of the irreducible polynomial GL-representations, alongside the Schur and Weyl functors, which is of independent interest.

We develop standard errors for estimates of causal effects in settings where the distribution of treatment exposures is known but potentially exhibits complicated dependence patterns across units. Such dependence arises, for example, in settings with spillovers/interference across units or when the treatment assignment is spatially correlated. Our variance estimator generalizes several properties of the Neyman variance estimator for completely randomized experiments to general designs: it is unbiased for an upper bound on the variance from the design-based perspective; the conservativeness of this upper bound depends on the heterogeneity of treatment effects; and it is also valid under certain forms of super-population sampling of the potential outcomes. Our estimator reduces to standard approaches in simple designs, such as the Neyman variance estimator in completely randomized experiments and the cluster-robust variance estimator in cluster-randomized experiments. We show that the proposed estimator is admissible among the class of quadratic-form variance estimators, and derive asymptotic conditions under which it is consistent for an upper bound on the asymptotic variance of the treatment effect estimator. In simulations and applications based on two empirical studies, one with peer effects and another with a spatially correlated treatment, we find that the proposed variance estimator performs well, and in some cases yields standard errors that are 2-3 times shorter than those of existing alternatives.

Translating visual brain activity into natural language offers a powerful window into human cognition and neural semantic representation. Most prior brain-captioning approaches project fMRI signals into language space using paired supervision. However, the widely used Natural Scenes Dataset (NSD) was built based only on image-fMRI pairs, while existing methods rely on MS-COCO captions as indirect textual supervision. Critically, during fMRI acquisition, participants observe only cropped image regions, whereas the associated MS-COCO captions describe full scenes. This mismatch creates a fundamental gap between neural representations and textual supervision, introducing an inherent semantic loss in NSD-based brain captioning. To mitigate this limitation, we reformulate brain captioning as Neural-Grounded Visual Captioning, where language is generated directly from visually grounded neural evidence rather than text supervision. We propose MindVLM, a framework that maps fMRI signals into subject-aware visual tokens and leverages a frozen vision language model (VLM) to produce interpretable and personalized descriptions. Instead of point-wise regression, MindVLM focuses on extracting semantically relevant visual cues from neural activity, naturally accommodating partial observability and inter-subject variability. Extensive experiments on NSD show that MindVLM consistently improves caption quality across multiple VLM backbones, including LLaVA-v1.5, Qwen2.5-VL, and Gemma3, beyond intrinsic model priors. Despite requiring neither text supervision nor an LLM during training and operating under an image-grounded inference paradigm distinct from conventional captioning methods, MindVLM remains competitive with supervised approaches, suggesting that subject-specific neural grounding provides an efficient, scalable, and interpretable path toward faithful brain-to-language generation.

Do lattice triviality, suspected Borel non-summability and the perturbative Landau pole exclude an interacting four-dimensional theory satisfying the Osterwalder–Schrader axioms and reproducing every renormalized coefficient of positive-coupling $O(N)$ $\phi^4$ theory? An example involving one real function separates vanishing cutoff limits along its allowed bare trajectories from a nonzero result obtained by renormalizing the coefficients first; an exponentially small correction preserves its expansion and removes the pole in its running coupling. For the massless two-point expansion of the singlet composite $\Phi_a\Phi_a$ at leading order in $1/N$, ordinary Borel summation fails even for Gaussian smearing. The arithmetic mean of two Borel integrals along opposite imaginary rays defines a real distribution on every four-dimensional Schwartz momentum or position test, with finite-order remainder bounds uniform on bounded test sets. Two alternative covariances with nonnegative mass spectral weights remove the Euclidean pole and construct generalized free fields. After a fixed contact subtraction, their Euclidean extensions preserve every coefficient of the collective correlations obtained by Wick pairing. The interacting finite-$N$ family remains open. We also state a conditional interacting route through the physical scalar correlations of a larger theory (the parent) with heavy particles. A concrete $N=1$ gauge–Higgs–fermion candidate has a tuned one-loop trajectory on which all interaction couplings tend to zero in the ultraviolet, and a stable tree vacuum with additional masses comparable to the heavy scale. Constructing the parent and its corrected ultraviolet trajectory, and proving coefficient decoupling and the exact remainder bounds as the quartic coupling tends to zero and the family's heavy masses grow, remain open.

The 5G-grade DECT NR+ technology designed to support massive machine-type communications (mMTC) relies on the decentralized mesh connectivity concept. The currently utilized topology construction algorithms are very sensitive to the node density, which causes interference at the node association phase and may lead to instable topologies. In this study, we propose several algorithms that need to be utilized at relay and leaf nodes to allow stabilization of the topology: (i) load-dependent relay allocation, (ii) hysteresis-based association control, (iii) blacklist-based association control, and (iv) smart beacon placement. Due to the complex interference structure in DECT NR+ mesh systems, we utilize system-level simulations to assess the performance in both normal and ultra-dense conditions in terms of the efficiency of topology construction and the performance characteristics of the resulting topology. Our results show that dense DECT NR+ networks do suffer from topology instability, with reassociation rates exceeding 10 per second and recovery times lasting over 10 minutes. By implementing the proposed mechanisms, the network dynamically scales, reducing the number of required relays by more than half, from 34% to 15%. They also stabilize the topology by reducing the reassociation rates to just 2-3 per second allowing large-scale networks of several hundred nodes to operate efficiently.

We consider planning for unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) teams in aerial monitoring missions with ordering requirements on the monitoring points to be visited by the UAV. The system consists of multiple UAV-UGV teams, each comprising one UAV and one UGV. UAV energy limitations are modeled through endurance, defined as the maximum flight time on a full battery. The UGVs serve as mobile charging stations and transport the UAVs between consecutive aerial tours. Given a set of monitoring points subject to ordering constraints and the teams' initial and terminal positions, the objective is to minimize mission completion time while satisfying UAV energy limits and the required visit order under bounded travel-time disturbances that may arise during execution. Unlike prior work, the plan jointly determines vehicle routes and their timing, allowing teams to slow down as needed to satisfy the ordering constraints. We develop a polynomial-time algorithm that generates efficient solutions to the underlying NP-hard planning problem. We establish feasibility guarantees, characterize the algorithm's computational complexity, and evaluate its performance via numerical comparisons.

Large language models are becoming central to GeoAI systems, yet their evaluation rarely considers the elicitation of geospatial data requirements. This omission is critical as retrieval oriented geo-analytic tasks cannot be supported reliably without first identifying the necessary datasets and constraints. GeoFitBench-LLM is introduced as a benchmark for assessing whether LLMs can infer the datasets, the supporting resources and the constraints required by geo-analytic requests in natural language. The benchmark is structured around two reasoning dimensions, Spatio-Temporal Relational and Semantic Grounding, reflecting long-standing challenges in geospatial information retrieval and related natural language tasks. Ground truth requirements are encoded in a fixed, provider-independent schema for reproducible evaluation of resource identification and attribute-level specification. Experiments on seven models under minimal prompting indicate that identifying the necessary resources is often achievable, with GPT-5.4 Thinking achieving the best result by recovering the complete set of resources in 66.67% of benchmark requests. Results further indicate that accurate fitness-for-use specification remains more difficult as inferential demands increase.

Language model agents increasingly operate over long interaction streams, requiring online adaptation to distribution shifts through continual learning. However, existing agent harnesses typically either evolve their states only through forward information flow or rely on additional replay or validation data for harness optimization. To address this, we propose ReHarness, a recurrent harness framework for agentic continual learning that complements forward read and write with backward revision under a strictly online streaming protocol. We ask what information could have been captured differently in the harness state to better inform the current instance in the stream. Specifically, after each instance, we leverage the resulting trajectory as feedback to revise the reflections retrieved for that instance, thereby propagating feedback backward through the textual harness state. Across three continual learning benchmarks and three language model backbones, ReHarness consistently outperforms strong raw-context baselines, memory- and reflection-based methods, and prompt optimization approaches. Further analysis shows that ReHarness produces source-grounded and meaningful revisions, corrects overgeneralized or outdated experience under distribution shifts, and improves both stability and plasticity during continual learning.

Large language model (LLM) evaluations on clean benchmarks overstate model robustness: real inputs arrive perturbed, and these meaning-preserving variants routinely move model answers. Studying this systematically requires applying perturbations one at a time, reproducibly, and identically wherever they run, yet existing tools couple them to a benchmarking stack rather than packaging them as a reusable transform layer. We present perturber, a stateless service and Python library that applies exactly one semantics-preserving perturbation per call, drawn from a first-party catalog of 68 perturbations across 11 families. It turns on a single primitive, with composition left to the caller chaining calls, so the service and the library produce identical output by construction. We evaluate the tool itself, its correctness, reproducibility, and cost, rather than any model's robustness, measuring meaning-preservation per perturbation rather than assuming it. The demonstration adds a live playground, an introspectable catalog for benchmark selection, and a one-command reproducible evaluation.

We introduce iRAG, a human-in-the-loop decision-support system combining Retrieval-Augmented Generation (RAG) with Hybrid Decision-Making. Unlike conventional RAG systems, relying on static Knowledge Bases (KBs), our proposal addresses settings where the KB is initially empty and is progressively populated through human decisions. The system stores previous decisions as retrievable precedents and moves from silent observation to evidence-grounded contestation and, finally, to autonomous handling with abstention. Against an independent baseline, iRAG matches final-decision error under 10% drift without retrieval decay and reduces it under 40% drift across all configurations. Retrieval decay improves performance on changed knowledge while increasing error on stable knowledge, evidencing a stability–plasticity trade-off rather than a general advantage. Human oversight is an architectural provision of the workflow; its usability with real human users remains to be evaluated.

The so-called “100% rule” is a somewhat classical and yet somehow obscure rule that gives some local sensitivity-analysis information based on the very limited local sensitivity-analysis information that is often made available by linear-programming software, derived from an optimal basis that is hidden from the user. Introduced in a classic undergraduate textbook in 1977, half a century ago, it was only picked up on by researchers in a very limited way, and while it appears in some undergraduate textbooks, it tends not to appear in most modern graduate-level textbooks. Our contributions are to celebrate and revive interest in the 100% rule and to extend it in a meaningful way. We introduce a cone rule that certifies primal feasibility for more right-hand sides than the 100% rule does, using the same information, and that can be applied in linear time. We then study when this cone rule is tight, that is, when it captures the entire cone of right-hand sides for which the basis remains feasible. We characterize tightness in every dimension for right-hand sides interior to that cone, make the characterization explicit for m=2 and m=3, and settle the question for tridiagonal bases in every dimension: tightness is impossible once m>=4, and for m=3 we give an explicit criterion in the entries of the basis. We give further results for symmetric, integer and unimodular bases. Finally, when tightness fails, we measure the fraction of the feasibility cone captured by the rule using normalized solid angles. For the autoregressive family at m=3, we obtain a closed-form candidate for the infimum of this fraction over all right-hand sides, whose optimality is supported numerically. We also obtain a closed-form expression for the best case over most of the correlation range, subject to two numerically verified properties, and estimate the best-case value numerically more generally.

We construct exact deterministic circuits for transposing and inverting an unknown qutrit unitary $U\in\mathrm{SU}(3)$ using only forward queries. Three queries prepare a catalyst independently of the input state. Four further queries implement transposition while returning the catalyst unchanged and uncorrelated with the output. Two uses within an antisymmetric encoding implement inversion with eight processing queries and return the same catalyst. Reusing the catalyst implements $m$ transpositions or inversions with $3+4m$ or $3+8m$ total queries, respectively. More generally, we prove that exact transposition and inversion of an unknown $U\in\mathrm{SU}(d)$, $d\ge2$, require at least $d+1$ and $d^2-1$ processing queries, respectively, in fixed causal order. These processing bounds hold for any program state prepared independently of the input state using finitely many forward queries, even if that state is consumed during processing. Both our catalytic qutrit algorithms attain their respective bounds. Moreover, exact qutrit transposition with four processing queries requires at least three preparation queries, and our construction attains this bound.

We develop an optimization algorithm for spherical lattice discretizations based on the spectrum of the discretized Laplace operator. Starting from refined icosahedral lattices, we minimize the splitting of the $(2\ell+1)$, $\ell=0,1,2,\dots$, continuum multiplets expected from $\mathrm{SO}(3)$ symmetry via gradient descent. This approach simultaneously produces lattices based on triangles with nearly uniform circumradii and perimeters. Although the optimization uses only the free-particle spectrum, we show that the resulting lattices carry over to interacting models. On the optimized lattices, rotational symmetry is restored for the critical Ising and Potts models and primary scaling dimensions are accurately reproduced for the three-dimensional Ising conformal field theory, when appropriate geometry-dependent interaction strengths are used. Higher-angular-momentum descendant states reveal weak residual symmetry breaking beyond the sectors protected by the underlying icosahedral symmetry.

Legacy Fortran physics packages in atmospheric models such as CESM, WRF, and E3SM pose a barrier to GPU modernization, while manual porting requires accelerator-programming expertise. We present LAFT (LLM-Assisted Fortran Translation), an agentic framework for converting Fortran atmospheric physics parameterizations into GPU-accelerated JAX while preserving numerical agreement with the Fortran reference. LAFT coordinates source-code analysis, translation, repair, runtime validation, and performance profiling. It combines a deterministic front end for metadata extraction and bridge generation, structured translation prompts, numerical validation, and profiling-guided feedback to identify inefficient execution patterns. The bridge handles array-layout conversion separately from scientific computation. We evaluate LAFT using the Kessler warm-rain microphysics scheme and four LLMs: Claude, GPT, Gemini, and Qwen. All four validated translations reproduce the Fortran reference outputs to near floating-point precision for the evaluated case, but their GPU performance differs substantially with execution design. The Gemini-generated implementation achieves up to a 357-fold speedup over serial Fortran in cached execution at 1,000,000 atmospheric columns, excluding compilation and host-device transfers. The results demonstrate that numerical agreement alone does not ensure efficient GPU execution and motivate combining numerical validation with hardware-aware performance analysis. LAFT provides a practical workflow for modernizing legacy atmospheric physics code through LLM-assisted translation, deterministic interface generation, automated validation and repair, and reproducible profiling.

GPU architecture research requires representative benchmarks that can execute on new designs. However, many vendor-tailored workloads and library kernels cannot run directly on research architectures because their implementations are closed-source or rely on programming models unsupported by the target architecture. Migrating existing kernels requires manual effort to adapt their implementations and validate their behavior. This creates a need to automate workload migration to target platforms. We present VortexSynth, a framework that uses profile-guided benchmark reconstruction to construct GPU benchmarks from reference workloads. Our workflow selects hot kernels through profiling, synthesizes implementations in the target programming language, verifies output equivalence, and measures profile differences using a translated proxy implementation. The resulting profile signature gap is supplied to an agent for iterative refinement. We evaluate the method on Vortex, an open-ISA GPGPU, using robotics as the application domain. All active kernel pairs pass both output-equivalence checks, and the case studies show that iterative refinement can reduce profile distance.

We introduce a new stochastic model of telomere length dynamics during hematopoiesis. The numerous cell divisions occurring in this setting makes telomere length dynamics, and in particular their attrition, a crucial aspect of hematopoiesis. After recalling the main aspect of the biological setting, we describe an individual based model of hematopoietic population cells. We then study its behaviour in the large population limit, as well as its fluctuations.

Data-centric scaling of RLVR has focused on collecting or generating verifiable training problems. However, corpus size alone does not determine whether the dataset provides a useful learning signal for a target policy. To guide the synthesis of effective RLVR data, we experimentally characterize dataset effectiveness as a function of its problems, the target policy, and the training rollout budget. Under this characterization, we show that a large open-source math corpus pooled from widely used RLVR datasets falls almost entirely into a zero-advantage trap: for a fixed target policy and rollout budget, roughly 88% of its problems are solved in every rollout or failed in every rollout. Filtering concentrates what remains, but it can only select, discarding the hard problems. Effective synthetic problems should therefore require the reasoning operations and compositions required to solve those hard problems. Yet their difficulty must be calibrated, so that some rollouts succeed, some fail, and at least one correct solution fits within the training budget. Prompting a teacher to vary hard problems directly does not achieve this. Guided by these empirical principles, we introduce MagicBeanStalk, a top-down decomposition and bottom-up recursive data-synthesis algorithm that grows seed problems into families of substantively new, policy- and budget-calibrated training problems while preserving the seeds' reasoning blueprints. Across 8 math benchmarks, continual RLVR on MagicBeanStalk problems improves gpt-oss-120b from 61.2 to 69.8 (+8.6) and DeepSeek v4Flash from 72.4 to 77.9 (+5.4) on a 16K-token budget. Training on the full 78K source corpus improves by only +1.1 and its best filtered real data subset by +5.8. In finance, we synthesize over 14K verifiable problems from only 340 solutions and improve over base by 6.9 and 2.4 points on SecQue and FinanceBench, respectively.