Papers

Learning from scientific measurements often requires aligning modalities with different spatial support and resolution. Subsurface characterization is an extreme dense-sparse problem in which 3D seismic provides volumetric but indirect measurements and well logs provide high-resolution 1D measurements at sparse borehole locations. We introduce a physically grounded cross-modal masked autoencoder (CM-MAE) for seismic-to-well representation learning. The model jointly tokenizes seismic volumes and well-log depth patches, embeds both modalities in continuous physical coordinates using four-axis rotary position embeddings, and reconstructs masked targets with a cross-modal decoder. Sparse Mixture-of-Experts layers provide modality-specific capacity while dense attention allows information exchange between modalities. Pretraining uses 23 seismic volumes covering approximately 178,000 square km across U.S. offshore and onshore basins, together with approximately 92,000 wells. Matched-mask ablations show strongly asymmetric information flow. Seismic context improves held-out well-log reconstruction by 9.73%, while well-log context improves seismic reconstruction by 0.65%. We evaluate seismic-only pseudo-log predictions against independent interpreter-drawn salt-geobody masks to determine whether they contain geologic signal. Across offshore U.S. surveys, compressional-slowness-derived salt scores reach an AUROC of 0.910. In onshore basins, predicted compressional slowness preserves formation-scale structure and partial relative organization in an unseen survey despite calibration drift. CM-MAE learns useful seismic-to-well representations under extreme modality asymmetry, although absolute pseudo-log calibration remains survey-dependent.

We study feasibility correction for linear programs. Suppose an initial point satisfies most of the constraints. Can it be moved into the feasible region without changing the objective value? Our main deterministic result says that this is possible if the constraint matrix satisfies a restricted isometry property (RIP). We apply the correction theorem to obtain lower bounds for random linear programs with finite-moment or sub-Weibull entries. We complement these with matching-order upper bounds under a uniform $p$th-moment bound for some $p>2$ and a delocalization condition on the objective direction. As an application of our techniques, we also derive lower bounds for the Gaussian width of feasible regions under RIP assumptions.

Climate change is intensifying natural hazards, and preparing cities for them falls primarily to local governments. Yet what municipal codes say about hazards, and whether their requirements match each city's risk profile, has not been measured. I analyze 3.6 million sentences from 204 U.S. cities' municipal codes and compare each city's hazard text to its actual risk from FEMA's National Risk Index. I document four patterns. First, a small share of code text consists of provisions relevant for natural hazards (1.5%), and codes in high-risk cities contain marginally more. Second, hazard coverage is highly concentrated on flooding (61% of hazard-relevant text), even though flooding accounts for only 9% of the average city's risk. Third, city codes emphasize emergency response over prevention. Emergency management is the largest regulatory category, and land use is the smallest. Fourth, codes track the types of risks relevant to each location, but only loosely. The median city would need to reallocate 70% of its regulatory text to match its risk profile. The results suggest that U.S. city codes do not include regulation for most of the hazards cities face.

Scientific figures are designed to communicate information visually, yet MLLMs typically explain them by translating their visual content back into text. This requires readers to manually map the resulting explanations back to the figure. Inspired by how people present visual information, we introduce FigAct, a framework that transforms static scientific figures into question-conditioned visual presentations by acting directly on their existing graphical elements. Like a human presenter, FigAct generates a sequence of short narrations, grounds each narration in the corresponding visual evidence, and applies visual actions to guide the viewer's attention. We develop a hierarchical search strategy for efficient element localization, reducing token usage by approximately 40$\times$. We further train FigAct-8B using three task-specific rewards for grounding accuracy, search efficiency, and rendering quality. We further build a human-verified benchmark from figures in real-world scientific papers to evaluate the ability of MLLMs to generate grounded visual explanations. Our results demonstrate the effectiveness of FigAct and show that treating scientific figures as presentation canvases makes explanations clearer and easier to follow.

Routine chest CT captures upper-abdominal structures that may contain clinically relevant incidental abnormalities. Detecting these findings requires feature extraction from organs with different spatial extents and attenuation patterns. We propose FD-AA, a lightweight organ-aware classification head adaptable for frozen 3-D CT encoders. Within each organ, an attenuation-aware module preserves sparse focal evidence, while masked generalized-mean pooling captures diffuse anomaly patterns. In seven abdominal organs, FD-AA with Pillar-0 achieved state-of-the-art (SOTA) performance in both the CT-RATE test set (AUC = 0.798) and the external RAD-ChestCT dataset (AUC = 0.713). More specifically, FD-AA improved macro AUC/AP from 0.763/0.346 to 0.798/0.405 over direct classification using frozen Pillar-0 only (p = 0.034/0.016). Such performance gain generalizes across multiple frozen encoders (AUC improvement on MedicalNet +9.8%, CT-CLIP +14.7%, ResNet +3.7%), demonstrating the effectiveness of FD-AA across different feature representations. These results support the effectiveness of integrating focal-diffuse aggregation with explicit HU evidence for incidental abdominal abnormality detection.

Let $k$ be a finite field of characteristic $p\neq 3$, let $E/k$ be the Fermat cubic curve, and let $\ell\neq p$ be a prime. If $p\equiv1\pmod3$, assume moreover that $\ell>3$. Then $H^3_{\mathrm{nr}}(k(E^3)/k,\mathbb{Q}_\ell/\mathbb{Z}_\ell(2))=0$ and the cycle map \[CH^2(E^3)_{\mathbb{Z}_\ell}\longrightarrow H^4(E^3,\mathbb{Z}_\ell(2))\] is surjective. In particular, $H^3_{\mathrm{nr}}(\overline{k}(E^3)/\overline{k},\mathbb{Q}_\ell/\mathbb{Z}_\ell(2))=0$. Assuming the Tate conjecture for surfaces over finite fields, we prove an analogous surjectivity result, for all but finitely many primes $\ell\neq p$, for the integral cycle maps for $1$-cycles on every smooth projective variety of dimension $d$ over a finite field of characteristic different from $2$ which admits a smooth projective lift to the ring of Witt vectors. We apply our results to a conjecture of Colliot-Thélène on the local–global principle for zero-cycles over global function fields. To further illustrate these results, we exhibit examples showing that vanishing of degree-$3$ unramified cohomology over the algebraic closure of the ground field does not imply vanishing over any finite subextension, not even for Fano varieties.

Symbolic Regression (SR) is a data-driven method for scientific discovery which searches for interpretable analytical relationships within data. Recently, Large Language Models (LLMs) have also had a significant impact on scientific discovery, enabling the automation of various stages of the process. For these reasons, the possibility of harnessing the embedded scientific knowledge and programming capabilities of LLMs to solve SR tasks has emerged, showing promising performance compared with traditional methods. We propose EvoMO-SR, a novel LLM-driven SR framework in which the LLM generates equation skeletons, with their coefficients fitted separately by an external optimizer. The framework includes a multi-objective survival selection which controls bloating by balancing accuracy and complexity, and a substructure guidance mechanism which mutates expressions with candidate reusable building blocks. EvoMO-SR achieves the best accuracy in seven of the eight in-domain and out-of-domain settings for LSR-Synth, using a small LLM model, i.e., Llama-3.1-8B-Instruct. We also evaluated structural recovery through two symbolic accuracy metrics based on canonicalized subtree overlap and term matching, showing that our method has a greater probability of recovering highly accurate symbolic structures.

For a graph $H$, $\langle H \rangle$ denotes the class of all subdivisions of $H$ and $tw(H)$ denotes the treewidth of $H$. In this paper, we prove the following. For $k\geq 1, R\geq 1$, let $G,H$ be two graphs such that strong isometric path complexities (Chakraborty et al. [Disc. Math., 2026]) of both $G$ and $\langle H \rangle$ are at most $k$, and $G$ admits an honest, “nicely rooted” $R$-bounded $H$-partition. Then, there is a graph $F$ with $tw(F)\leq tw(H)$ such that $G$ admits a $(1,33\cdot R\cdot k^2)$-quasi-isometry to $F$. Using results of Albrechtsen, Distel, and Georgakopoulos (2025), we also obtain that $K_{2,t}$-asymptotic minor-free graphs admit quasi-isometries with additive distortion to $K_{2,t}$-minor-free graphs. This answers an open question raised by the above authors. As part of our proof, we combine the graph-partition based method and the layering partition based method (Chepoi et al. [Discrete Comput. Geom. 2012]) to obtain additive quasi-isometry when both the source and all subdivisions of the target graph have bounded strong isometric path complexity.

Data from conventional diffusion tensor imaging (DTI) using single-shot echo planar imaging (SS-EPI) acquisition are substantially influenced by magnetic field inhomogeneities (delta B0), which result in image distortion and signal dephasing. Multi-shot EPI can mitigate the delta B0-induced artifacts but at the cost of increased scan time. Recent brain tissue-selective, dynamic slice-by-slice B0 shimming techniques have demonstrated effective reduction of local delta B0 in the brain. When combined with DTI utilizing an echo-planar imaging (EPI) read-out, image distortion and signal dephasing are significantly reduced. The purpose of our study was to assess the impact of DTI with dynamic slice-by-slice B0 shimming technique (DySiBo) on white matter (WM) tractography. We retrospectively analyzed DTI datasets using SS-EPI and Multi-shot EPI with 2 shots (MS-2shot-EPI) readout at two spatial resolutions (1x1x2mm3 and 2x2x2mm3) with and without DySiBo. WM tractography was generated and inspected to examine the impact upon regions typically affected by delta B0-induced artefacts. We found more WM streamlines were generated in the DTI datasets with DySiBo in regions conventionally impacted by delta B0-induced in EPI images, including the brainstem, temporal and frontal lobes. DySiBo substantially improved the generation of WM streamlines in DTI-based tractography at both in-plane resolutions. In conclusion, DySiBo in conjunction with DTI requiring 10 diffusion tensor directions is sufficient to generate data with high enough SNR and angular resolution to resolve crossing fibers and produce high quality WM tractography in brain regions typically affected by susceptibility-induced artefacts. This has implications for quantitative WM microstructural indices and clinical evaluation of WM tracts in patients.

The local dark matter (DM) velocity distribution is significantly altered by the gravitational impact of the Large Magellanic Cloud (LMC), which creates a high-velocity tail. We evaluate how the LMC reshapes the DM landscape for a wide variety of theoretical models in light of the recent putative LZ DM event. We show that the LMC-induced velocity shifts substantially modify the parameter space for inelastic endothermic DM models across a broad range of possible interactions, driving the viable regions towards larger mass splittings, which are more susceptible to collider and indirect detection constraints. By contrast, models for elastically colliding DM are less impacted, and some remain viable candidates – for example, the simple light Singlet-Doublet Majorana DM candidate at the Higgs blind spot. Our work confirms that accurately accounting for LMC effects is essential when high-velocity DM is probed, rather than relying on the simplified Standard Halo Model.

Stellarator ideal magnetohydrodynamic (MHD) codes that assume nested flux surfaces such as VMEC and DESC solve the equilibrium problem by prescribing the total toroidal magnetic flux, plasma profiles and the last closed flux surface (LCFS), which analytically determines the unique field in vacuum, whereas at finite $\beta$ bifurcations and distinct equilibria sharing the same boundary have been reported in the literature. In this paper, we propose prescribing the Poincaré cross-section of the field at a single toroidal plane, and implement it in DESC, where the new condition enters only through the linear constraints and therefore costs no more than a fixed-LCFS solve. Fixing the geometry on one plane rather than on a full toroidal surface generally leaves more of the spectral coefficients free, and the ones it frees are those carrying the toroidal variation of the boundary flux surface, which a prescribed LCFS holds fixed at every toroidal angle; together these allow better-converged numerical solutions. We solve equilibria with the cross-section held fixed, starting either from the axisymmetric shape obtained by revolving that cross-section toroidally, or from an existing fixed-LCFS solution. In the latter case, the volume-averaged normalized force error falls by an order of magnitude while the configuration stays close to the original one, and re-solving the resulting boundary with the conventional fixed-LCFS solver recovers the same equilibrium. We further show that the Poincaré coefficients can be used directly as design variables by optimizing a quasi-helical configuration that maintains high-fidelity force balance throughout the process.

Robot manipulation policies are usually trained under the assumption that a commanded action produces the same motion as it did during training even after hours of operation. Real hardware violates this assumption as the motors gradually heat up, current saturates near contact, voltage sags under load, thus the same policy action can produce a weaker, delayed, or noisier motion. These conditions are already measured by onboard telemetry, such as joint temperature, motor current, and supply voltage, yet this signal is typically used only for logging or safety checks rather than policy adaptation. We introduce Telemetry-Aware Action Rectification (TeAR), a policy-agnostic method that turns a frozen manipulation policy into a telemetry-conditioned policy by rectifying its outgoing action before it reaches the low-level controller. TeAR learns a lightweight Transformer that combines the proposed action with live actuator telemetry and amplifies, damps, or biases individual action components. We evaluate TeAR across 18 policy-task pairs spanning 8 policy families and 5 manipulation tasks. In an additional paired evaluation with degradation-model mismatch, TeAR achieves 31.8% success, compared with 25.6% for the base policy and 30.6% for an assumed-model inverse. On a physical arm, TeAR improves success under heating by 10-15% without on-robot fine-tuning.

The algebra of polysymmetric functions (PSym) is defined as the tensor product of copies of the algebra of symmetric functions (Sym) where the $i$th copy has variables scaled by $i$. One way to construct a basis of PSym is to start with a basis $\{f_\lambda\}$ of Sym and consider all pure tensors arising from this basis. Asvin G and Andrew O'Desky described four families of non-pure tensor bases, namely $H, E, E^+$ and $P$, which we call plethystic bases. In this paper, we study the expansions of the plethystic bases into the pure-tensor bases $\{h^\otimes_\tau\}$ and $\{e^\otimes_\tau\}$, and interpret the results via combinatorial objects called polywrapping block tabloids. The expansions of $H, E$ and $E^+$ in $h^\otimes$ and $e^\otimes$ are found via the $h$-expansion of the plethysm $h_n[p_r]$. We compute this $h$-expansion using a statistic on words and prove it through abacus methods.

We describe the Macaulay2 package MixedHodgeModules, which computes Hodge and weight filtrations on localizations S_f of a polynomial ring S at a non-constant reduced polynomial f, as well as on twisted localizations S_f f^{-\alpha}, where \alpha\in QQ is rational. The package includes functionality for computing Hodge ideals, weighted Hodge ideals, higher multiplier ideals, generation levels of Hodge filtrations, weight levels of elements, p-functions, and lengths of weight filtrations. It also provides routines for computing graded de Rham complexes, Du Bois complexes, and intersection Du Bois complexes of hypersurfaces.

While the amount of telecommunications services grows rapidly in the whole world, humans get potentially more exposed to Non-Ionizing Radiation (NIR) from a number of different sources. This paper has a number of goals, including monitoring radiation levels in an everyday situation, an investigation of how national and international regulations organs address NIR levels and a demonstration of scientific production trends regarding this topic. The work also presents a bibliometric study about the main scientific productions and trends related to NIR measurements, with focus on the field of Telecommunications. Another contribution is a case study in Natal, Brazil, where NIR levels were monitored in four distinct locations over a period of 24 hours each and compared to the current regulations. The result is a quantitative analysis of the amount of radiation that some populations might be exposed to in distinct moments of the day. Measurements were carried out in the proximity of an antenna spot, since it could represent a source of high NIR levels (a worst case of human exposure). This campaign differs from older studies by including a more intense usage of microwaves frequencies due to operating 4G and pre-5G systems in Brazil. Finally, a statistical study involving the measurements is conducted, concluding the analysis of how some population groups might be affected by NIR.

Group Relative Policy Optimization (GRPO) has become a promising approach for training large language model agents. However, its uniform assignment of trajectory-level advantages to all policy tokens fails to distinguish consequential decisions from less relevant ones, obscuring which intermediate decisions contributed to success. We introduce ProVer, a framework that targets potentially pivotal decisions for fine-grained credit assignment in agentic reinforcement learning. Given a rollout group, an agentic judge contrasts successful and failed trajectories to propose a segment potentially responsible for their divergent outcomes. Rather than directly trusting the judge's assessment, ProVer verifies the proposed segment by estimating its advantage from the difference in terminal success rates between current-policy continuations sampled before and after the segment. Positive estimates are then incorporated into the GRPO advantages of policy tokens within the proposed segment. By using model judgment only to select where to verify, ProVer grounds local credit in observed outcomes without exhaustively evaluating every intermediate state. Across ALFWorld, WebShop, and SearchQA, ProVer achieves the strongest average performance at both model scales, with relative improvements over GRPO of 9.91% and 7.12% for Qwen3.5-2B and Qwen3.5-4B, respectively. Further analyses demonstrate that informed segment selection improves policy training with modest additional generation overhead, even without a frontier-scale judge model, highlighting the effectiveness and efficiency of selectively targeting pivotal decisions for fine-grained credit assignment in agentic reinforcement learning.

We compare two natural proportional notions of a risk component's contribution to the aggregate tail risk of a collection of risks: the fraction of aggregate tail risk capital allocated to the component under Conditional Tail Expectation (CTE), and the component's expected realized share of aggregate risk under Geometric Tail Expectation (GTE). The resulting proportional allocations generally differ. For arbitrary random vectors-allowing atoms, signed risks, and any tail domain–we establish when the allocations agree, determine their ordering when they do not, and characterize their asymptotic separation. Both proportional allocations are weighted averages of the conditional risk share of a component given the aggregate: the proportional CTE allocation weights tail scenarios by severity, whereas the proportional GTE allocation weights them uniformly. Their difference is therefore a normalized tail covariance. The proportional CTE and GTE allocations agree throughout a tail exactly when the conditional risk share is constant there; under a mild unimodality condition, dominance is characterized by its monotonicity. Among independent exponential dispersion models with heterogeneous natural parameters, exact agreement is possible only for the scaled Poisson family; under comonotonicity, it is equivalent to proportional quantile functions. In the extreme tail, the limiting relationship between the proportional CTE and GTE allocations is governed by the ratio of Expected Shortfall to Value-at-Risk: boundedness ensures common limits, convergence to one forces the allocations to merge, and divergence can cause their limits to separate.

The growing development of online educational video resources over the past two decades, has significantly reshaped university students' self-regulated study approaches and influenced diverse ways of learning. Within an environment of abundantly and publicly available online resources, educators cannot always control which materials students choose to supplement their study. Consequently, considerable deviations are likely to be present between the taught content by the educator and an arbitrary online educational video the student watches, in terms of terminology, notation and methods, especially in mathematical sciences. These deviations can be even more considerable when Transnational Education (TNE) students incorporate native language resources to comprehend the material. This paper presents the design, creation and implementation of interactive video resources produced in alignment with established pedagogical frameworks to support an undergraduate TNE mathematics module.

Tablet-based teaching and learning has become increasingly common in university mathematics courses, offering capabilities such as digital ink, dynamic visualisation, and real-time annotation. However, there is limited experiential evidence regarding how students perceive the specific benefits and drawbacks of tablet-supported teaching and learning, particularly in Transnational Education (TNE) settings. This paper presents results from a small-scale exploratory survey of undergraduate students ($n = 19$) attending mathematics courses within an applied sciences degree programme, who anonymously rated a set of statements regarding their experiences with tablet-based instruction on a five-point Likert scale. Initial analysis shows that students in this cohort perceived tablet teaching most positively in supporting step-by-step understanding and active engagement during lectures through real-time annotation and structured note-taking. In contrast, perceptions related to long-term recall, interest in mathematics, and preference over alternative teaching methods were more mixed. These findings suggest that students in this cohort perceived tablet-based teaching positively for supporting procedural understanding, while perceptions of other aspects of learning appeared more varied.

We consider fair resource allocation in sequential decision-making environments modeled as major-minor weakly coupled Markov decision processes (M2WCMDP). In this framework, resource constraints couple the action spaces of a major sub-Markov decision process (sub-MDP) and a population of minor sub-MDPs that would otherwise operate independently. Instead of using the traditional utilitarian (total-sum) objective, we optimize a general class of monotone, concave, permutation-invariant, normalized fairness functions. With homogeneous minor sub-MDPs, we prove that the problem under symmetry reduces to optimizing the platform-plus-mean-participant utilitarian objective over the class of permutation-invariant policies, which allows us to exploit efficient algorithms that optimize the utilitarian-based objective to solve this fairness-aware problem. For more general settings, we introduce a count-proportion-based deep reinforcement learning approach with a priority-based sampler that generates feasible count actions. The generality of our framework means that the proposed algorithms and theoretical guarantees transfer to any domain with a symmetric M2WCMDP structure. We consider two applications: the machine replacement problem and the joint control of pricing and taxi relocation problem on a New York City-calibrated dataset. We validate our theoretical findings with comprehensive experiments, confirming the effectiveness of our proposed method in achieving strong fairness-aware performance while remaining scalable.

Parallel speculative drafting generates multiple candidates in one backbone pass, but independent token selection can produce inconsistent continuations that shorten the accepted prefix. Existing methods mostly leave conditional decoding to a lightweight module after the backbone, which limits the flow of predecessor information to successors. Our analysis of DFlash shows that early positions already form recoverable predictions in shallow layers, and that accurate adjacent predecessors help successors more when they enter earlier. We therefore propose DSpine, a drafter with causal conditioning injection throughout the backbone: at every layer, gated adjacent injection writes each predecessor's predicted feature into its successor, so the causal conditioning chain unfolds over network depth while all positions update in parallel. A unified transfer space built from the target model's output embeddings unifies layer-wise injection with predecessor-conditioned decoding, and layer-wise output-embedding supervision promotes the formation of predicted features in shallow layers. Fused kernels and a transition cache execute both efficiently in parallel within SGLang. Across seven math, code, and chat benchmarks, DSpine achieves the longest acceptance length at both temperatures on Qwen3-4B and Qwen3-8B. At temperature zero on Qwen3-8B, it raises the seven-benchmark mean from DFlash's 3.77 to 4.82 (+27.8%); in SGLang serving tests, it delivers 23.3% higher throughput than DFlash on average. Project page: https://dspine-project.github.io

Figuring out how objects relate to each other, like whether they touch, overlap, stay completely separate or one sits inside another, matters a lot in fields like GIS, biomedical imaging, and robotics. Even though machine learning has come a long way, people haven't really focused on spotting these topological relationships in images. The main roadblocks? Not enough good datasets and no clear way to measure results. So, we rolled up our sleeves and built a new dataset. It's pretty sizable: over 11,000 labelled images showing all those essential relationships. We ran tests with some classic machine learning models, Naive Bayes, KNN, Random Forest, SVM, and Artificial Neural Networks, and threw in some deep learning stars like VGG16 and InceptionResNetV2. For the dataset itself, we used segmentation, contour detection, and grayscale normalization to tease out solid feature vectors. The results? Deep learning methods, especially VGG16, pulled ahead, with validation accuracy hitting 89.55%. That's a big jump compared to the traditional models. This shows how powerful transfer learning is for analyzing topological relationships in images, and it gives researchers a new standard to aim for in future work on spatial reasoning and topological classification.

Large-scale demonstrations have driven unprecedented progress in robot learning, yet collecting robot data through teleoperation is expensive and difficult to scale to diverse environments and long-horizon tasks. Simulation offers a scalable alternative, but existing data-generation pipelines often rely on open-loop controllers, scripted skill sequences, or task-specific programs. We introduce SkillWeaver, an agentic framework that autonomously generates robot experience by exploring over Neural Interaction Skills (NIS): reusable, parameterized, closed-loop policies that expose learned physical interaction capabilities to a reasoning agent. Given a task and a simulated environment, a VLM agent reasons about what to do next, invokes and parameterizes NIS to interact with the environment, observes their outcomes, and generates verification, reflection, and memory to guide subsequent exploration. We instantiate NIS as reinforcement-learned policies for closed-loop, contact-rich manipulation and organize exploration as verifier-guided tree search, enabling the agent to discover successful long-horizon behaviors without relying on predetermined execution pipelines. SkillWeaver scales autonomously to 39.1K demonstrations across 14.1K scenes, which we distill into visuomotor policies. Across simulation benchmarks and real-world manipulation, training on SkillWeaver-generated experience substantially improves generalization to novel objects, spatial configurations, tasks, and environments, and enables zero- and few-shot sim-to-sim and sim-to-real transfer. Our results suggest agentic exploration over neural interaction skills as a scalable alternative for robot data generation.

AI coding agents fail in two coupled ways. They spend most of their context window rediscovering where things live, and they assert success without evidence when the work gets hard. Repository indexes address the first with cheap context, and orchestration frameworks with adversarial review address the second with accountability. Both describe the same object, the structure of the codebase, at two timescales: what is true of the code now, and what was verified to be true, at which revision, by whom. Assay makes that observation operational. Every claim an agent makes (tests pass, no secrets, behavior preserved) is bound to the Merkle hash of the dependency cone of the code it covers, so the claim is stale exactly when that code or anything it depends on changes. We show the binding is sound and minimal, and that the blast radius of a change is precisely the set of claims it invalidates. On the graph we place a risk-proportional evidence obligation, a bounded review protocol with separation of duties, and a merge gate that consults no model: coverage, freshness, signatures, exit codes, plausibility, evidence monotonicity (the mechanical form of "do not delete the failing test"), and review status. Assay is a dependency-free Python tool with an MCP server. On five public repositories a 600-token brief costs 14x to 114x less than an exploration proxy, warm rebuilds are up to 5x faster than cold ones, cone binding re-verifies 7.9% to 81.9% of claims where repository binding re-verifies all of them while per-module binding misses 23% to 68% of required invalidations, and the gate blocks 9 of 9 scripted adversarial behaviours while admitting the honest ones. Every number in this paper is generated by the released scripts.

The cores of neutron stars have a combination of density, temperature, and neutron-proton asymmetry that cannot be replicated in laboratories or understood using first-principles quantum chromodynamics. Thus, observations of neutron stars are necessary to understand this regime. In particular, precise and accurate measurements of neutron star radii are highly informative about cold, catalyzed matter at a few times nuclear saturation density. X-ray observations with NASA's Neutron star Interior Composition Explorer (NICER) have yielded radius measurements for a few nonaccreting neutron stars, which have advanced substantially our understanding of dense matter. In this review we discuss the NICER radius measurements and their implications and demonstrate that the systematic errors thus far explored in NICER analyses have at most a minor effect on the inferred radii of neutron stars.

Depth completion aims to recover dense metric depth from sparse sensor measurements, increasingly leveraging visual foundation models as geometric priors. However, aligning these priors to true metric scale typically relies on rigid affine assumptions in predefined coordinate systems, leaving systematic calibration errors. Linearity in depth calibration depends on the response coordinate. We introduce adaptive response geometry, which makes the fixed choice of depth, log depth, or disparity an image-level unknown. A continuous response family unifies these coordinates and defines an explicit depth-dependent gain. We derive the response-gradient relation and estimate the response parameters in metric space. Hard-Dirichlet residual reconstruction completes the calibrated prior. Under deliberately incomplete metric observations, the training-free pipeline achieves macro AbsRel 0.0301 and macro NMed 14.04{\deg}, improving both aggregate measures over PriorDA, LDCM, and Any2Full. Linearity diagnostics examine how the selected response changes the depth relation and its metric error.

Distributed Denial of Service attacks are a growing threat to network infrastructure, and new techniques, including the use of generative AI, make them harder to detect. Traditional detection systems, such as rule based firewalls, often fail to identify these evolving attack patterns. In this study, we propose a new method for detecting DDoS attacks by combining synthetic data generation using Generative Adversarial Networks with a Random Forest classifier. The GAN generated data showed 80.3 percent cosine similarity to real traffic, which helped the model learn underlying traffic patterns more effectively. To address imbalances in the data, especially in packet related features, we applied adversarial debiasing. This reduced the model's sensitivity to skewed distributions in variables such as forward and backward packet counts and total byte lengths. Our results show that models trained on a mix of synthetic and real data achieved significantly better performance: 99.98 percent accuracy on benchmark data and a 22.60 percent improvement when tested on previously unseen synthetic traffic. This suggests that the method can generalize well across different traffic scenarios and adapt quickly to new types of attacks. The proposed approach not only improves DDoS detection but also provides a scalable foundation for security models that account for bias and benefit from data augmentation. Our findings show that combining GANs with adversarial debiasing can lead to more robust and effective DDoS mitigation, supporting the further development of machine learning based cyber security.

Lattice materials have highly tunable mechanical properties that are controlled by their internal geometry and base material behavior. While fracture models for low-density lattices are well-established, the fracture of lattices at relative densities above 30% remains largely unexplored. Here, we present an analytical model that combines homogenization methods and blunt-crack fracture theory to predict the fracture toughness of triangular and hexagonal lattices over a wide range of relative densities. Finite element modeling corroborates the analytical framework and demonstrates a shift in failure mechanisms between low and high relative density regimes. At high relative densities, failure is dominated by nodal stress concentrations, which are strongly influenced by the local crack-tip geometry and the macroscopic crack path. Significant stress redistribution is observed as the relative orientation and lattice fillet radius are varied, resulting in increased fracture toughness relative to baseline geometries. Furthermore, quasi-brittle poly(methyl methacrylate) (PMMA) lattices achieve about a 1.6x enhancement in fracture toughness relative to perfectly brittle lattices as failure is delayed by localized plasticity. Notably, some quasi-brittle lattices are found to exceed the fracture toughness of their base material – a feature only possible when the cell size is large compared to the base material's plastic radius. Experiments on lattice fracture specimens made from laser-cut PMMA validate the finite element results, but highlight the stochastic nature of failure in brittle lattice materials, especially at higher relative densities.

In this work, we develop a second-order optimization framework for physics-informed neural networks (PINNs) applied to high-dimensional parametric partial differential equations (PDEs). The framework is built on the Gauss–Newton pullback metric, which provides an operator-informed notion of curvature in parameter space and connects the method to the broader family of natural gradient schemes. We show that, for coordinate-separable neural architectures and linear differential operators (or linearized operators in the nonlinear case) admitting a finite separable representation, the residual Jacobian inherits a structured separable factorization. This yields an exact compressed formulation of the Gauss–Newton step in a reduced space, without assembling the full residual Jacobian on the exponentially large tensor-product collocation grid. The dimension of the reduced space (the effective compressed dimension) is determined by the local collocation grid sizes, the separable operator structure, and the contraction pattern of the architecture, thereby avoiding dependence on the full tensor-product grid size and replacing dense linear algebra in parameter space by a substantially smaller structured problem. Within our framework, we investigate canonical polyadic and tensor-train parametrizations and derive their full algebraic characterization relevant to the Gauss–Newton method, including the structure of the residual Jacobian, the resulting compressed system, and its effective compressed dimension. Numerical experiments on high-dimensional PDEs, including parametric problems, demonstrate the high efficiency of the proposed compressed Gauss–Newton method, which achieves substantially lower errors than tensor-compressed first-order baselines with orders of magnitude fewer iterations and only a fraction of the computing time.

This work presents a Non-Ionizing Radiation (NIR) measurement campaign and proposes a specific measurement method for trajectography radars. This kind of radar has a high gain narrow beam antenna and emits a high power signal. Power density measurements from a C-band trajectography radar are carried out using bench equipment and a directional receiving antenna, instead of the commonly used isotropic probe. The measured power density levels are assessed for compliance test via comparison with the occupational and general public exposure limit levels of both the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the Brazilian National Telecommunication Agency (Anatel). The limit for the occupational public is respected everywhere, evidencing the safe operation of the studied radar. However, the limit for the general public is exceeded at a point next to the radar's antenna, showing that preventive measures are needed.