Papers

We present an algorithm for handling the small cell problem in Cartesian cut cell grids. The advantage of this variation is that it preserves the base scheme's steady state exactly. We show several computational examples using finite volume schemes in two space dimensions.

In this note, we show that over a geometrically irreducible smooth projective curve over an infinite field $k$, the moduli stack of semistable vector bundles of fixed determinant is $\mathbb{A}^1$-connected if and only if the moduli stack admits a $k$-rational point. For this we use Langton's elementary modifications for vector bundles at the level of families. In addition, we prove the $\mathbb{A}^1$-connectedness of the moduli stack of symplectic bundles with forms valued in a fixed line bundle $L$ on a smooth projective curve of genus $g \ge 2$ over an infinite field $k$ with $C(k)\neq \emptyset$. As an application, we deduce the $\mathbb{A}^1$-connectedness of moduli stack of quasi-parabolic symplectic vector bundles with forms valued in a fixed line bundle.

Designing custom Cerrobend collimators for linac-based preclinical electron irradiation is labor intensive and susceptible to design inconsistencies. We developed Collimator Creator (CC), an open source parametric workflow that converts aperture dimensions and jig offsets into printable STL models for a collimator mold, collimator shell, Cerrobend holder, and beam degrader. Two designs were fabricated and characterized: a 4.0 x 1.5 cm$^2$ bilateral lung collimator centered on the central axis and a 1.5 x 1.5 cm$^2$ unilateral lung collimator with a 7.5 mm jig offset, each with a 15 mm thick Cerrobend collimator and a 10 mm PLA degrader. Kilovoltage planar images were used to assess aperture geometry and casting uniformity. Radiochromic film was used to measure full width at half maximum (FWHM) and 80%-20% penumbra under conventional and ultra high dose rate (UHDR) electron delivery on a Varian TrueBeam, and off axis leakage was measured with an ionization chamber at conventional dose rate. The cast Cerrobend apertures deviated by less than 0.2 mm from their specified designs. FWHM values were within 3% of the nominal field dimensions, and penumbra ranged from 0.73 to 1.05 mm under conventional and UHDR delivery. Crossline leakage 2 cm beyond the collimator edge was below 2% for both collimators at conventional dose rate. Parametric collimator generation standardized digital design inputs for the two evaluated rectangular linac-based electron fields. Further work will assess specimen-level dosimetry, additional aperture geometries, and Monte Carlo integration.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ”internal mode”. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical $\phi^4$ model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the $\phi^4$ model.

We prove a noncommutative maximal ergodic inequality for averages along polynomial sequences. Let $\gamma$ be a trace-preserving automorphism of a semifinite von Neumann algebra $(\mathcal N,\tau)$. We show that the associated polynomial averages \begin{equation*} A_Nf:=\frac1N\sum_{n=1}^N\gamma^{P(n)}(f), \qquad N\in\mathbb N, \end{equation*} satisfy a strong maximal inequality on $L_p(\mathcal N)$ for every $1<p<\infty$, extending the previously known restricted range of $p$. The proof follows Bourgain's major-arc strategy but requires substantially new ideas and tools for operators that may have further applications in noncommutative analysis. More precisely, we obtain a localized maximal inequality by developing a noncommutative version of Stein's extrapolation, novel combinatorial methods, and a surprising multilinear version of Doob's maximal inequality. For the required decaying $L_2$-approximation, we combine two of Bourgain's constructions in a way that avoids the multi-frequency maximal inequality used in the scalar proof.

The rapid advancement of LLM agents has enabled systems to autonomously perform complex tasks through external tools, but their growing access to personal data introduces significant privacy risks. Existing benchmarks primarily evaluate LLM agent privacy through simulated trajectories and outcome-based metrics, limiting their ability to capture privacy risks arising during multi-step agent execution. In this work, we introduce AgentPrivArena, a framework for evaluating privacy risks in realistic LLM agent workflows. AgentPrivArena integrates authentic MCP tools and self-hosted services within a reproducible execution environment. We further propose trajectory-level privacy metrics that quantify unnecessary information access beyond final response leakage. Building on this framework, we introduce AgentPrivAudit, a runtime auditing approach for monitoring privacy violations during agent execution. Extensive experiments on state-of-the-art LLM agents reveal substantial privacy risks overlooked by existing evaluation paradigms, highlighting the importance of trajectory-level auditing for trustworthy agent deployment.

Time Series Foundation Models (TSFMs) achieve strong generalization by learning to reconstruct or forecast broad temporal patterns from large-scale time series during pre-training. Yet this strength can become a weakness for anomaly detection: TSFMs may model rare anomalous patterns as effectively as normal ones, allowing anomalies to be accurately reconstructed or forecasted and thus diminishing their reconstruction/forecasting error-based anomaly scores. This paper proposes $\underline{\textbf{N}}$$\textbf{ormality}$ $\underline{\textbf{C}}$$\textbf{onstraint}$ $\underline{\textbf{L}}$$\textbf{earning}$ ($\textbf{NCL}$), a lightweight plug-and-play framework that adapts pre-trained TSFMs for accurate anomaly detection without modifying their pre-trained parameters. Our key insight is to constrain the broad pattern space of TSFMs to the normal structure of a target time series, preventing their broad modeling capability from obscuring abnormal deviations. Specifically, NCL constructs a compact normality subspace from a few normal patch features and adaptively steers each patch feature toward normality within this subspace, guided by contrastive constraints that form compact and discriminative normality manifolds. The calibrated features are aggregated to reinforce normal components and fused with the original TSFM output, amplifying the discrepancy between normal and abnormal observations for the reconstruction/forecasting error-based anomaly scoring. Extensive experiments across diverse TSFM families and benchmarks show that NCL consistently improves anomaly detection performance, providing a generalizable framework for adapting TSFMs to anomaly detection.

VLM safety is commonly evaluated through input- and output-level classification. Such classification is necessary, but it does not reveal whether a safety state is accessible or controllable inside the model. We argue that multimodal safety evaluation should therefore report a controllability profile alongside behavioral classification, separating representation-level detectability, cross-modal specificity, intervention sensitivity, and benign-preserving selectivity. Using implicit toxicity as a stress case, we instantiate this profile on LlavaGuard and Qwen3.5 with sparse feature decompositions. LlavaGuard admits localized handles with a narrow benign-preserving intervention range and modest downstream safety gains, whereas Qwen3.5 supports strong representation-level readout but no comparable selective-control regime under the tested operators. These results show that internal readout and controllability can diverge. Future multimodal safety benchmarks should therefore report not only behavioral safety metrics, but also whether safety-relevant internal signals can be intervention-tested and controlled within a validated operating range.

Photonic quantum technologies require the integration of high-quality quantum light sources with programmable photonic circuitry to enable on-chip quantum information processing. Semiconductor quantum dots have emerged as a leading platform for quantum light generation, yet their monolithic integration with cryogenic-compatible, programmable photonic circuitry remains challenging. Here we demonstrate a programmable quantum photonic platform that enables simultaneous control of highly coherent quantum dot-based single photon emitters and reconfigurable optical elements at cryogenic temperatures. System-level integration enables individual electrical and optical addressing of active components on a single chip, allowing their concurrent operation while preserving coherent non-classical light emission. We demonstrate multiple quantum-photonic functionalities, including pure single-photon generation, two-photon interference, and resonant transmission and reflection measurements of integrated emitters. These results mark a step from isolated quantum-optical devices towards programmable quantum-photonic hardware platforms capable of combining coherent quantum emitters with large-scale photonic functionality.

Foundation models (FMs) are increasingly being developed for general time series and physiological signals, yet their transferability to downstream physiological tasks remains poorly understood. This question is particularly challenging for electromyography (EMG), where signal distributions vary substantially across users, sensing configurations, acquisition hardware, and downstream tasks. We introduce EMG-FM-Bench, a systematic benchmark for studying foundation-model transfer and adaptation on EMG. EMG-FM-Bench unifies 20 public datasets with over 1 million EMG segments and evaluates nine pretrained foundation models across four questions: how pretrained models perform when frozen or fully fine-tuned, how much pretraining helps compared with training the same model from scratch, how well models generalize to new users with limited labeled data, and how performance changes across different EMG tasks. Across the benchmark, linear probing provides useful information about pretrained representations, but full fine-tuning can substantially change downstream EMG performance. Comparing each pretrained model with the same model trained from scratch shows that the benefit of pretraining varies substantially across models and is not universal. Performance decreases when models are evaluated on new users, while five-shot adaptation improves macro-F1 in 70.2% of evaluated model-dataset combinations but recovers only part of the lost performance. Model performance is highly consistent between upper- and lower-limb classification and remains strongly correlated with continuous EMG-to-text decoding. Together, these results provide a systematic view of when pretrained time-series models transfer effectively to EMG and how their performance depends on fine-tuning, user variation, and downstream task.

Does any integer survive in the shift current, and does the Chern number control its sign? We show that the shift vector is a singular field on the Brillouin torus. Its curl has two sources: the interband Berry curvature and quantised point charges at the zeros of the transition dipole. Inverting this relation gives an exact decomposition of the shift conductivity, valid at every frequency, into one sector linear in the integer charges and three continuous sectors. As a testing ground, we take a graphene-Haldane bilayer: a model that lets us sweep the interband Chern number through five values at fixed gap to isolate its role. We also test the formalism against the time-reversal-symmetric biased AB bilayer. Whenever a charge sits at the band edge, and trigonal warping is present, the integer sector alone accounts for the band-edge peak. The relevant integer is not the Chern number but the winding of that single charge. Its sign, combined with a valley-dependent profile, sets the sign of the photocurrent. In these bilayers, sign reversals across topological transitions follow this winding; the invariant changes with it only when the same gap closing does both. A band-edge charge needs no invariant. It only requires that the two band-edge sublattices not be connected by the nearest-neighbour hopping, and trigonal warping makes it visible.

The Variational Quantum Eigensolver (VQE) has become a central hybrid quantum-classical method for addressing electronic structure and materials science problems on near-term quantum hardware. As researchers across physics, chemistry, and quantum information engage with VQE, they encounter a wide range of algorithmic choices, including problem encoding, ansatz construction, classical optimization, and measurement strategies to choose from. This article provides a structured overview of these components and discusses practical factors that influence VQE performance in real settings, such as noise characteristics, available error-mitigation techniques, and hardware-dependent circuit considerations. Drawing partly on our early experiences, we highlight aspects that may be especially relevant for newcomers and outline common challenges observed in practical workflows. Our aim is to offer an accessible entry point for researchers approaching VQE-based quantum simulation and to support informed decision-making as the method and underlying hardware continue to evolve, which we support by discussion of examples from physics and quantum chemistry.

Deploying model predictive control (MPC) requires constructing or identifying a predictive model for each target system. Time-series foundation models (TSFMs) offer an attractive option thanks to strong zero-shot forecasting capabilities across systems. However, low forecast error does not guarantee that a TSFM captures the system's response to the alternative actions considered by the controller. We study this gap using residential heat-pump control as a test bed, measuring the agreement between predicted and ground-truth effects of control interventions. Importantly, we find that TSFMs can recover the system's input-response relationship when the context contains sufficient independent control excitation. Common fine-tuning pipelines and feature smoothing reduce, but do not eliminate, the need for in-context excitation. Our results indicate that current TSFMs used for predictive control require sufficiently informative control variation in the inference context. Initial closed-loop results show promise for shorter context windows.

Large language models (LLMs) trained to answer questions are natively poor at teaching. Reinforcement Learning (RL) against a simulated student is a promising approach to improve their pedagogy, but existing RL-trained tutors reward the student's success on the tutored problem with the tutor's words still in context. The reward is then easiest to raise by telling the student the answer, and a tuned penalty is needed to reduce telling. Drawing on learning sciences, we introduce a masked near-transfer post-test: the student is tested on an unseen variant of the tutored problem with the tutor's utterances masked, so the reward can rise only through what the student wrote in its own turns. This discourages cognitive offloading by the student and allows the continuous penalty to be replaced by two binary reward gates (factual correctness of tutor response, no solution handover). A leave-one-out ablation shows that the learning-gain reward on its own does not separate teaching from telling: the gates reduce solution handover while the near-transfer post-test improves out-of-domain transfer. Using these reward designs we develop Eduardo, a multi-turn RL recipe for training LLM tutors, and use it to train 4B, 9B, 14B and 27B models from two distinct LLM architectures. Our post-trained Eduardo-27B model matches Gemini-3.1-Pro on MathTutorBench and Claude Opus 4.8 on TutorMoments at 2.4-6.2x fewer thinking tokens than frontier models, which matters for interactive tutoring. Without being named in the reward, the model more than doubles its use of the push-for-justification teacher move while support fading (e.g., assigning independent work), whose payoff lies beyond a single-problem dialog episode, is trained out. We open-source our training environment, an 8,671-problem near-transfer dataset, and trained models for further development.

Let $q=2^n$ with $n\ge6$, and let $\mathbb{F}_q$ be the finite field with $q$ elements. For a subspace $E$ of $\mathbb{F}_q$, define \[ S(E)=\sum_{x\in E\setminus\{0\}}x^{-1}.\] Let $N_{n,k}$ denote the number of $k$-dimensional $\mathbb{F}_2$-subspaces $E$ for which $S(E)=0$. We prove that, if $k\ge3$ and $n\ge2k+1$, then \[ \left|\frac{2^nN_{n,k}}{\genfrac{[}{]}{0pt}{}{n}{k}_{2}}-1\right|<2^{r^2+r}2^{n(1-r/2)},\] where $r=\lfloor\frac{k-1}{2}\rfloor$, and $\genfrac{[}{]}{0pt}{}{n}{k}_{2}$ is the Gaussian binomial coefficient. In particular, \[ N_{n,k}\sim2^{-n}\genfrac{[}{]}{0pt}{}{n}{k}_{2}\quad (n\to\infty)\] uniformly for $n/3<k\le(n-1)/2$. Combined with the known low-dimensional cases and the symmetry between dimensions $k$ and $n-k$, and the elementary middle-dimensional subfield construction, this proves a conjecture of Carlet: for every $3\le k\le n-3$, there exists a $k$-dimensional $\mathbb{F}_2$-subspace $E$ such that $S(E)=0$.

Around 30% of global energy expenditure can be attributed to the building sector, where a large portion of energy-consumption could be avoided by repairing existing faults. Fault detection and diagnosis (FDD) software addresses this issue; however, its creation and operation also have an environmental impact. The magnitude of this impact is influenced by the diagnosis architecture, as different architectures and methods have different energy demands. Yet, simply considering the energy consumed by the software itself is not sufficient to assess its overall environmental impact, since the diagnostic performance, e.g., number of detected faults or number of faults missed, also contributes to its ecological footprint. In this paper, we propose an energy-consumption model that considers FDD performance and energy spend directly by the diagnosis software. In an initial experiment, we compare several FDD architecture families, i.e., rule-based, model-based, classical machine learning, and large-language-model-based, in simulation using performance and energy-consumption values collected from prior literature. The results show that considering the computational energy and accuracy of FDD can change the relative benefit of the different approaches. Computationally efficient machine learning methods, such as random forest, provide the largest net savings on smaller buildings, whereas more resource-intensive approaches, such as fine-tuned large language models, become advantageous as building size increases. Our findings suggest that overall energy efficiency depends not only on the computational demand of the FDD software, but also on its diagnostic performance and the scale of the building.

The high cost of functional molecular assays, and prevalence of missing modalities and unmatched samples in computational biology, create significant barriers to comprehensive multi-omic profiling, essential for capturing and reasoning over molecules, cells, tissues, and organisms. This work proposes a model that learns meaningful representations from multi-omics cancer data supporting the reconstruction of missing and unpaired modalities. Contrary to increasingly complex, larger models, e.g. Foundation Models (FMs), ARO prioritizes practical applicability in limited or incomplete data settings. ARO optimally reconstructs missing modalities (MSE of $0.15$ on the validation and test data in the Unmasked settings), with its learned latent embeddings enabling a downstream cancer classification task. Our findings indicate that analyzing diverse molecular layers as a single integrated system offers a reliable and cost-efficient approach, reducing dependence on large-scale experimental testing, while still supporting multi-omic exploration in limited data settings.

We study torus surgery on the Cartwright–Steger surface and the degree-two cover construction proposed in \cite[Remark~1]{ASY}. Every torus in this surface is integrally nullhomologous, and surgery on a fixed disjoint collection of such tori cannot decrease the first Betti number. We then determine the nodal-curve subgroup and complete the fundamental-group calculation in the degree-two construction. The resulting minimal symplectic manifold has signature zero and fundamental group $\Z/2$; for compatible symplectic gluings, its universal cover is an exotic symplectic $31\CP^2\#31\overline{\CP}^{\,2}$. The construction on the original Cartwright–Steger surface gives a minimal symplectic manifold with signature $-1$ and fundamental group $(\Z/2)^2$.

We consider weak solutions $u \in W^{1,n}(U,\mathbf{R}^{n+1})$ of the $H$-system $- \operatorname{div} ( |\mathrm{D} u|^{n-2} \mathrm{D} u ) = (H \circ u) \, \mathbf{J} u$, where $n \ge 2$, $U$ is the open unit ball in $\mathbf{R}^n$, and $H$ is bounded. We show that $u$ is locally bounded if its distortion $|\mathrm{D} u|^n / |\mathbf{J} u|$ is bounded on the set where $|u|$ is large. By a result of Fusco, Kristensen, Leone, and Verde, it follows that $u$ is locally Hölder continuous if $H$ is continuous, and continuously differentiable with locally Hölder continuous derivative if $H$ is locally Lipschitz. The proof pushes forward $|\mathrm{D} u|^{n-2} \mathrm{D} u \circ \mathrm{D} u^*$ by $u$ to a linear functional on continuous compactly supported maps of $\mathbf{R}^{n+1}$ into $\operatorname{Hom}(\mathbf{R}^{n+1},\mathbf{R}^{n+1})$, whose values on derivatives are controlled by the equation. When the distortion is bounded, this functional satisfies the hypotheses of an inequality of Michael-Simon type for measures satisfying a first-order partial differential equation, due to De Philippis, Gennaioli, Pigati,and Rindler. The inequality yields lower bounds for the mass ratios of the push-forward of $|\mathrm{D} u|^n \mathscr{L}^n$ by $u$, and these imply boundedness.

We use the breeding technique to construct genus-3 Lefschetz pencils for which the total spaces have $c_1=0$. We compute the fundamental groups of our Lefschetz pencils and identify them with the fundamental groups of certain torus bundles over tori. Using work of Friedl and Vidussi, the total spaces of our pencils are homeomorphic to torus bundles over tori. These bundles do not admit sections.

What happens when a legal AI model learns to look like a lawyer instead of reasoning like one? We fine tune Qwen3-8B with Group Relative Policy Optimisation (GRPO) against a proxy built from three surface features: citation count, legalese density, and response length. The model does not learn to reason more effectively. It learns to withhold commitment. Across 16 yes or no legal reasoning tasks from LegalBench (N=320), overall accuracy collapses from 0.500 (chance) to 0.072 (McNemar p < 10^-36), driven entirely by the rate of properly formatted answers falling from 0.900 to 0.109. The model stops committing to answers. Yet when it does commit, accuracy rises from 0.556 to 0.657, showing that the collapse is not a failure of capability but a strategic response: the model has learned that verbose responses packed with citations but empty of a direct answer score higher than terse correct ones. We term this the Saul Goodman effect, a policy that becomes maximally lawyerly while becoming maximally noncommittal, and prove formally that it is the optimal response to any surface feature proxy that attaches no penalty to abstention. We further show that 89.3% of citations produced after training are structurally implausible hallucinations, many of them subtly corrupted names of real landmark cases, constructed in effect to survive a casual read and fail under scrutiny. To detect this failure mode before deployment, we introduce three diagnostic tools: the Confidence Theater Score (CTS), the Citation Plausibility Rate (CPR), and the Regret Gap (RG). In a domain where a confidently wrong answer can constitute malpractice, the broader lesson is direct: a reward function that measures how legal a response looks will produce a model that is maximally photogenic and minimally useful.

In this paper, we study closure relations of Simpson strata in Hodge moduli spaces over a smooth complex projective curve of genus $g\geq2$ and prove in every rank that the Heinloth weight strictly increases whenever a specialization changes the fixed component. For stable full chains, we refine this numerical condition by comparing the degrees of the corresponding filtration steps and construct counterexamples to Simpson's nestedness conjecture for the Dolbeault and de Rham moduli spaces in every rank $n\geq4$. Using the maximum property of this weight, we also discuss Simpson filtrations from the viewpoint of $\Theta$ stratifications.

We introduce Heuristic-Guided Fourier Fine-Tuning (HeuFouFT), a task-guided framework for selecting trainable frequency coordinates in Fourier fine-tuning. Existing uniform and Gaussian band-pass schemes allocate a limited spectral budget through fixed, task-agnostic rules. HeuFouFT instead searches for coordinates using downstream performance. A coarse intensity map from lightweight block-level probes initializes three metaheuristic optimizers: Genetic Algorithm with Simulated Annealing (GA-SA), Particle Swarm Optimization (PSO), and Cuckoo Search (CS). During search, a Random Forest filters each population so that only the top 30% of candidates proceed to proxy fine-tuning. On E2E with GPT-2-Medium, all three variants outperform random-uniform FourierFT, Gaussian band-pass FourierFT, and LoRA across five metrics. PSO further outperforms LoCA, the best-performing baseline, on four metrics while using 37.6% fewer trainable spectral coefficients. Once coordinates are selected, HeuFouFT requires only 15–18% FLOPs of Full FT. These results show that task-guided search allocates limited spectral capacity more effectively than fixed sampling. Our code is publicly available.

Nanoscale imaging of developing plant cell walls is expensive, and a limited number of atomic force microscopy (AFM) scans cannot capture the full structural variability of the wall. We present a generative-physics workflow that links sparse AFM observations of cotton (Gossypium hirsutum) fiber cell walls at 8 days post-anthesis (DPA) to distributions of effective elastic properties and a larger-scale mechanical response. We adapt a Stable Diffusion model with Low-Rank Adaptation (LoRA) to expand the experimental scans into an ensemble of AFM-like microstructures and assess the synthetic structures using microfibril crossover count and crossover angle. Each microstructure is mapped to spatially varying Young's modulus and Poisson's ratio fields and analyzed using strain-controlled finite element homogenization. Repeating this process across the image ensemble and a prescribed sweep of matrix-to-fibril stiffness ratios produces distributions of effective Young's modulus and Poisson's ratio. A single constitutive pair cannot capture this variation. The resulting distributions depend strongly on the matrix-to-fibril stiffness ratio and, in several cases, exhibit apparent multimodality. We further propagate the paired effective properties into 20 stochastic realizations of a tensile simulation of a larger specimen, yielding a distribution of macroscale stress response. The framework provides a probabilistic link between sparse nanoscale observations and continuum-scale mechanics while retaining variability across scales. The present results establish the computational workflow, while calibration of the intensity-to-property mapping against nanomechanical measurements remains necessary for quantitative prediction at the fiber scale.

The classical Descartes' rule of signs bounds the number of positive roots of a real polynomial in one variable by the number of sign changes of its coefficients. This bound only depends on the order of the exponents and on the signs of the coefficients, that is, on the oriented matroids of the exponent and coefficient matrices. We give a multivariate generalization of this rule to arbitrary fewnomial systems: for systems of $n$ real polynomial equations in $n$ variables with $n+k+1$ monomials, we obtain upper bounds for the number of nondegenerate positive solutions which only depend on sign conditions on the maximal minors of the coefficient matrix and of the exponent matrix and its liftings. For $k=1$ they are the Descartes rules of signs for circuits of Bihan-Dickenstein and Bihan-Dickenstein-Forsgård. Our approach starts from the Gale duality and the Khovanskii-Rolle argument of Bihan and Sottile, which reduce the problem to counting common zeros of iterated Jacobians in a polyhedron $\Delta$. This polyhedron is a chamber of a hyperplane arrangement whose combinatorics is determined by the oriented matroid of the coefficient matrix. We bound the number of these zeros by the Bézout number minus the zeros forced in the other chambers by a topological degree, which we compute by a facet-count formula involving the signs of minors of a Gale dual matrix of the exponent matrix. This leads to a recursion over the flats of the arrangement, which ends on lines with the Descartes rules for circuits. In this way the coefficients enter the bounds through the combinatorics of the arrangement, and the exponents through sign conditions on minors.

Predicting patient-specific survival functions is crucial for clinicians in making informed decisions about patient care and treatment strategies. Among the various models available, the Survival Forest has demonstrated significant effectiveness in numerous scenarios. In this work, we propose an ensemble method that leverages the strengths of the Survival Forest as the master model, complemented by several base models. This ensemble incorporates the Beran estimator, a type of kernel estimator, to enhance predictions of patient-specific survival curves. We evaluated the performance of our proposed model using four distinct healthcare datasets. The results highlight the superiority of our ensemble method over baseline models in both calibration and ranking across most datasets. The findings suggest that our approach offers a more accurate and reliable estimation of patient-specific survival functions, providing a valuable tool for clinical decision-making.

Low-power speech recognition requires reducing audio acquisition and feature-processing costs as well as neural inference. We present Lyric, a speech-recognition front end that uses wave-domain computing to extract features before digitization. Our proposed system uses passive acoustic resonators to separate speech by frequency and supplies their slowly varying envelopes to a compact temporal neural network. This moves spectral filtering into the acoustic structure, reducing the data and processing needed for recognition. We build a prototype and evaluate spoken-digit recognition on a speakerdisjoint AudioMNIST split across nine classifier families. The front end acquires 32 times fewer scalar samples than a 16-kHz waveform. In the EdgeSpeechNet-A comparison on a Raspberry Pi 4, we reduce preprocessing-plus-inference latency and estimated processor energy per inference by 98.6%, with a 3.58-percentage-point decrease in accuracy to 95.70%.

Numerous agentic workflows are based on a generator-verifier loop: a generator proposes candidates, a cheap verifier scores them, and the workflow terminates when a proposal is verified as good enough. The verifier typically proxies a more costly ground-truth oracle, and as the generator searches adaptively against it, false acceptances may accumulate. Proposals can pass the proxy but fail under the costlier ground-truth check. We study when to stop these loops while controlling the false discovery rate of the accepted proposals. Our construction introduces tools of independent interest in distribution-free statistical testing and conformal risk control, including analysis of $e$-values constructed through index betting and a novel conformal risk control procedure for non-monotone losses. We validate the approach in synthetic settings and on a protein-design benchmark.

Homogeneous numerical integration (HNI) combines Euler's identity and Stokes' theorem to integrate homogeneous polynomials over a polytope $P$. Existing algorithms return scalar integrals or reusable moment families. Any resulting moment table can be recoded afterward: once all degree-$q$ moments are known, integration on $\mathcal H\_q$ (degree-$q$ forms) has a trivial representation by a pure order-$q$ distribution supported at any single arbitrary point. Our contribution is instead to propagate functionals through the face complex, once for $(P,q)$ and without first forming the moment vector, to obtain a signed vertex-derivative coefficient functional on $\mathcal H\_q$, specific to $P$ and determined directly by its supplied face geometry and chosen anchors. A finite-dimensional Riesz framework describes its nonuniqueness, gives an intrinsic $L^2(P)$ error for restricted formulas, and supports weighted post-processing. The independently generated degree-$q$ and degree-$2q$ coefficient vectors satisfy an explicit compatibility relation. Vertex anchors can prune the propagated representation as shown in some polygon examples and an offline benchmark quantify this effect without claiming global cardinality optimality or improved conditioning. The construction covers convex polytopes and oriented non-convex polyhedral domains in arbitrary dimension.

Regional accent cues can be captured under matched conditions, but it remains unclear whether they persist between read and spontaneous speech. We study RVG1, with 500 German speakers from nine regions, comparing ten speech representations on regional classification and continuous geolocation under matched conditions and speaker-independent read–spontaneous transfer. Whisper performs best under matched conditions, reaching 0.489 nine-way UAR and 148 km median geolocation error, but drops to 0.11/0.18 UAR across transfer directions and 363 km geolocation error. Self-supervised models show a similar degradation, whereas speaker embeddings are less discriminative in-domain but more robust under transfer. This contrast is consistent across classification and geolocation. Across representations, robustness is associated with how little a representation shifts between styles (style-invariance), for which crossstyle speaker retrieval is an interpretable proxy. Age, sex, sentence-overlap, and duration controls do not account for the gap, although channel characteristics contribute. These results show that strong matched-condition performance does not indicate robust regional information.