Papers

Many release rules accept a lot when a statistic built from the sample mean and standard deviation stays within a limit, and the probability that a process passes such a rule can be computed exactly for a broad class of parent distributions. This paper asks how well that probability is itself known once the parent has been estimated. Under a stated reference posterior the answer is an interval, narrow where a lot clearly passes or fails and wide where it is contested. In ninety-eight published content-uniformity lots that position, not the sample size, sets the width: among the forty-eight lots assayed at the same ten units, and so equally informed about the spread, the $95\%$ interval runs from essentially zero width to $0.96$. With the operating point held fixed while test and estimation sample grow together, the interval narrows only slowly, the contraction of the posterior being offset by the steepening of the operating characteristic; a calibrated study at the sample sizes of $1207$ occupational exposure assessments shows the same under a half-plane rule. For a pure-spread rule under a Normal parent the interval has an exact chi-square form in the plug-in value and the two sample sizes, extending to the mean-spread wedge with a measured residual and containing Bergum's lower bound as one endpoint. With the parent's posterior formed from the same published summaries through the evaluator's own likelihood, the qualitative pattern survives but shape moves both endpoints and width: on the same lots a strong right skew lowers the pessimistic endpoint by up to a fifth and widens the interval by up to $0.22$. At the content-uniformity operating point studied, under a Normal parent, the symmetric error bar in standard use puts the lower endpoint $0.21$ too high and returns an upper endpoint above one, even with the full posterior covariance.

The performance of modern computing systems is heavily bottlenecked by the widening gap between processing throughput and main memory latency, a problem exacerbated when an application's logical data access patterns misalign with the physical layout of data in memory. To address this, we propose a hardware-software co-design framework comprising the Data Transformation Language (DTL) and the Data Transformation Unit (DTU). DTL allows programmers to concisely express complex data layout reorganizations, which the compiler translates into efficient hardware routing configurations. The DTU, a hardware engine logically situated between the Last-Level Cache (LLC) and main memory, transparently evaluates these configurations on-the-fly to gather scattered data elements into dense, logically contiguous cache lines. By converting explicit layout transformations into virtual views, this approach eliminates the need for explicit data materialization in software. We evaluate the DTU within a quad-core RISC-V SoC using FireSim, demonstrating substantial improvements in execution speed and memory efficiency.

The practicality of realizing high-directivity sources is studied using a generalized sensitivity metrics. These measures are based on the error model adopted in previous studies on array tolerance, but account for heterogeneous array characteristics in an arbitrary source-expansion basis, making it applicable to the study of continuous sources, ideal uncoupled arrays, and heterogeneous arrays with mutual coupling. The formulation provides the ensemble average of realized directivity under the selected error model, making it a fast predictor of anticipated directivity reduction due to source perturbation. The data required to compute these predictions are straightforward to obtain via simulation or measurement, with a significant simplification when the system can be approximated as lossless. The directivity and the proposed tolerance measures allow for the formulation of optimization problems illustrating the tradeoff between these measures. Several examples demonstrate these tradeoffs, special cases, comparison to previous estimates of maximum directivity, and the accuracy of sensitivity as a predictor of statistical performance over large ensembles of design realizations.

Batch risk-based inspection scheduling struggles to detect a critical failure class: food facilities with recent clean inspections that subsequently develop severe violations. Traditional systems recompute risk on fixed planning cycles using static historical data, leaving blind spots between inspection cycles. To address this, we introduce the Continuous Inspection Risk (CIR) system, an event-driven scheduling pipeline that re-ranks the inspection queue dynamically as new data arrives. CIR combines a decay-weighted historical score with a stream of real-time consumer reviews triaged by a language-model classifier. A key structural contribution is our temporal partition rule, which strictly excludes reviews predating the most recent inspection to prevent superseded signals from skewing current risk. Evaluating CIR on 9,505 routine inspections in Santa Clara County, California (2024-2026), we show that history-based scoring alone reduces mean time-to-detection of major violations by 69 days (20.9%) under a 30% inspection budget, but fails to anticipate severe vermin-related closures (0/8 detected). Incorporating post-inspection review signals drastically improves performance, predicting 7 of 8 vermin closures with an average lead time of 117 days-firing on the exact day of review publication in four instances. Introducing a review corroboration rule improves precision from 0.70 to 0.78 without loss of recall. Finally, we analyze critical implementation challenges, documenting a data-hygiene pitfall (stale review leakage across inspection boundaries) and an evaluation limitation involving unobserved facility self-remediation. This work provides the first case-level evaluation of event-driven inspection triggering using open data and provides a reproducible benchmark for review-augmented public health systems

Ionic liquids are materials whose properties can be tailored for a wide range of applications, but their chemical diversity and complex electronic structure make systematic screening using quantum-mechanical methods computationally demanding. Semiempirical quantum methods offer an alternative, although their accuracy depends on their parameterization. We investigate the reparameterization of the DFTB method GFN1-xTB for predicting structural, energetic, and electronic properties of ionic liquids. For this purpose, we built a database containing over 14,000 conformations to construct training datasets and explored different parameterization strategies fitted to binding energies, forces, HOMO-LUMO gaps, and geometries. Analysis of the original GFN1-xTB model reveals systematic errors in these properties, with distinct behavior for saturated and aromatic cations. Thus, we investigate two models: CXMIM-xTB, a targeted model trained on imidazolium-based ionic liquids, and IL-xTB, a more general model designed to describe systems containing saturated and aromatic cations. CXMIM-xTB improves the description of binding energies, geometries, and frontier orbital energies while retaining computational efficiency. The model is subsequently applied to estimate electrochemical windows of ionic liquids, providing values consistent with DFT and experimental values. IL-xTB follows a hierarchical parameterization strategy including different cation and anion families and substantially reduces the systematic errors of GFN1-xTB across the chemical space considered, providing a route for developing xTB parameterizations with broader applicability to ionic liquids. Overall, both parameterization strategies outperform the original GFN1-xTB model, demonstrating that reparameterized methods provide an efficient approach for connecting configurational sampling with quantum-mechanical properties of ionic liquids.

Van der Waals heterostructures offer a direct route to couple an optically active layer to a two-dimensional spin sensor, yet their coherent nonlinear response at interfaces remains poorly resolved. Here, we use polarization-resolved second harmonic-generation imaging to resolve four distinct regions of a hexagonal boron nitride (hBN) -based heterostructure, native hBN, neutron-irradiated hBN containing negatively charged boron vacancies (VB-), PbI2 and their complete overlap. The detected intensity scales quadratically with incident power, consistent with a dominant second-order optical process. Polarization scans show that adding PbI2 transforms the distorted VB- SHG anisotropy into a predominantly fourfold response with a sixfold stronger SHG than native hBN alone. This non-additive nonlinear response occurs in the same layer architecture also shown to enhance defect photoluminescence, linking spin-defect sensitization to an interface-modified effective second-order susceptibility.

Royen's Gaussian Correlation Inequality (GCI) is a fundamental result in statistics and probability, but unfortunately, at least by now, the result is not very well known in the statistical community. In this paper, we demonstrate the potential of GCI in high-dimensional testing problems that involve multivariate Gaussian variables. Leveraging the GCI, we establish sharp Type I error bounds under arbitrary Gaussian covariance structures. We also formulate a conjecture and relate it to the well-known Spherical Cap Covering Conjecture in discrete geometry and Weak Simplex Conjecture in information theory.

Join ordering is classic problem in data management. We highlight the connection between structure-specific dynamic programming algorithms and the mathematical enumeration of the possible merge trees from a join graph. We present two case studies, on double-star and helix shaped join graphs, that we believe carry useful techniques for a toolbox of building structure-specific join optimizers. For the double-star case, we show how the enumeration leads directly to a significantly improved search algorithm, whereas for the helix case we show that a algorithm derived from the mathematical enumeration is not necessarily better than structure-agnostic algorithms.

Retrieval-augmented generation (RAG) reuses the same documents across many requests, making non-prefix KV-cache reuse attractive. Yet a cached document state is not reusable text: it is a context-conditioned causal state whose keys and values depend on the prefix, position, and preceding documents under which it was computed. We formulate non-prefix KV reuse as a behavior-preservation problem with full prefill on the exact prompt as the reference, and introduce SAFE-KV, which repairs a composed cache by re-encoding the causal suffix from a selected start document. On Qwen2.5-7B-Instruct, prefix-conditioned composition preserves only 47.2% of HotpotQA-500 and 37.8% of 2Wiki-500 full-prefill answers; SAFE-KV with risk-guided K2 selection restores 99.8%/98.4% (donor-copy protocol) and 100.0%/98.4% with actual suffix forwarding. Document-only and fixed-window repairs recover far less, because the document states after the repaired region keep histories that omit it. Reuse without repair is exact up to four documents and degrades at sixteen, where suffix repair recovers 98-100%. Faithful repair re-encodes most of the context, so in a single-request L40S study SAFE-KV's operating rule serves every workload by full prefill. SAFE-KV thus establishes the causal-state contract for non-prefix reuse and a validated repair mechanism that meets it.

Test-time memorization of sequential information is a foundational capability for any intelligent system that needs to rapidly store and retrieve data, as demonstrated by the attention mechanism in large language models. However, Transformers and linear attention variants are trained via backpropagation through time (BPTT), which has drawbacks such as its enormous memory requirements. Predictive coding (PC), an algorithm that optimizes a prediction-error energy function with local updates, offers a compelling solution but still lacks test-time memory for sequential data. We develop a solution to this problem by treating the per-step memory update $\Delta S_t$ as a latent variable, as opposed to a slow weight to be learned. By taking the log probability of a standard PC-based probabilistic model, we derive a PC-native solution for verbatim sequence memory, and relate our update rule to common choices in the linear attention literature (e.g., DeltaNet). We present an extensive set of empirical tests to probe our system's properties, including its scaling capacity, memory footprint, and ability to infer a context from evidence (e.g., bank (river) vs. bank (money)). We show how DeltaNet-PC can be used for storing single sequences of data, multiple sequences of data, and key-value associative memory pairs with perfect recall accuracy.

Sparse near-field arrays phase-cohere $M$ widely separated sub-arrays of $N$ elements and underpin distributed MIMO, satellite formations, and integrated sensing and communication. We show that their interference suppression over a protected region is set by coherence within a single sub-array rather than by the span of the formation: the effective rank of the region covariance can collapse from $MN$ to $M$. Two independent arguments establish this. For canonical line and disk regions each diagonal covariance block is exactly a classical concentration operator, which supplies sharp per-block rank thresholds and makes fewer than one spatial degree of freedom per sub-array a conservative design rule; an orthogonal decomposition with eigenvalue interlacing gives a nonasymptotic sufficient condition that assumes nothing about the coupling between platforms. The consequences are covariance-side and beamformer-independent: the unloaded Capon functional upper-bounds worst-case signal-to-interference ratio, while its regularized counterpart scales very differently for angularly separated and for in-cone targets. An eight-satellite LEO study validates the theory, including realized worst-case SIR.

The rapid proliferation of distributed energy resources (DERs) aggregated by virtual power plants (VPPs) elevates cybersecurity risk by expanding the attack surface. A coordinated cyberattack has the potential to disrupt distribution-system, bulk-system, and market operations. Existing cyberphysical defense strategies largely assume access to grid network models and operating conditions, which may not be available to third-party aggregators. This paper proposes a novel hybrid, perturbation-based cyber-physical defense for VPP-operated DERs that blends game-theoretic planning with model-free reinforcement learning (RL) under a Bayesian belief-update framework. Topology agnosticism is defined from the VPP information and implementation perspective: the VPP does not require access to the feeder topology, line parameters, switching configuration, or full system state. This work advances the state of the art through three contributions: (1) a multi-output Gaussian process with Hamiltonian Monte Carlo for discrete attacker-type inference, probability of detection, and confidence of detection for modeling the belief distribution; (2) moment-matched Gaussian propagation of posterior beliefs across episodes; and (3) an RL policy that adaptively integrates Stackelberg leader (VPP) actions with exploration. Furthermore, we establish equilibrium existence and derive an episode-level closed-loop utility bound connecting attacker-belief uncertainty with GT-RL action alignment. Evaluations on IEEE 13- and 123-Bus feeders with DER portfolios demonstrate effective detection under attacker-model uncertainty and evaluated feeder re-configuration conditions, while requiring no explicit feeder-topology knowledge. Overall, the results indicate that combining bi-level game-theoretic planning, nonparametric Bayesian inference, and adaptive RL is a promising direction for VPP cybersecurity.

Is a chromosome a miniature of its genome, with the same mix of functional elements as the whole? We ask this of eight annotated genomes: human, mouse, zebrafish, Caenorhabditis elegans, Drosophila melanogaster, Saccharomyces cerevisiae, Arabidopsis thaliana and maize. Elements are classified in a four-level hierarchy, from five major classes (protein-coding genes, ncRNA genes, transposable elements (TEs), pseudogenes, IG/TR gene segments) down to finer classes. Units are chromosomes or arms, cytogenetic bands, equal cuts of each chromosome, and random segments of matching size. We compare each unit with the genome and with other units, call compositions homogeneous when they differ by less than 5%, and score each against a random sample of the same size. The first finding is a surprising homogeneity. The level-1 compositions of the major chromosomes match each other and the genome in maize, zebrafish, yeast and C. elegans, and in fly down to the major arms. Finer classes can be homogeneous too: protein function in Arabidopsis, and the Wicker TE orders in maize. Enzyme reaction classes are interchangeable between chromosomes in all eight genomes. The second finding is a structured heterogeneity. Where a unit departs from its genome, it does so in one of three ways: clusters of named elements, such as rRNA genes or immune receptor loci; megabase-scale compartments, such as TE-rich pericentromeric heterochromatin; and lineage-specific gene families, visible only at the finest levels. Corrected for chance, the genomes fall into groups. For protein function and gene families, composition is more uniform in plants and fly than in vertebrates, and least uniform in C. elegans. For the major classes and TE orders, uniformity follows where each genome places its repeats, along the arms (maize, zebrafish) or around the centromeres (Arabidopsis, fly), not its lineage.

Word-aligned prosody is increasingly used to detect depression and posttraumatic stress disorder (PTSD), yet the stability and clinical relevance of these measurements remain unclear. We examine stability at two levels. At the word level, we ask whether a speaker produces the same word in a similar speaker-specific way across different utterance contexts. At the speaker level, we ask whether averaging prosody across many words produces consistent speaker scores across separate recordings. Drawing on principles of psychological measurement, we compare these representations in four corpora spanning acted, spontaneous, and clinical speech. Word-specific deviations show little cross-context recurrence (0.01-0.16), whereas speaker summaries are highly consistent, reaching 0.997 in ESD, 0.73-0.90 in MSP-Podcast, and 0.84-0.996 in DAIC-WOZ and PTSD-STOP. Despite this consistency, associations with depression or PTSD severity do not exceed 0.15; equivalence tests exclude effects of 0.30 in all analyses and 0.20 in DAIC-WOZ, while within-person associations with daily PTSD symptoms are near zero ($|\rho|\leq0.04$). Thus, aggregation yields stable speaker-level prosodic measures, but these measures do not detectably track depression or PTSD severity in the studied corpora. Code is available at https://github.com/jen900704/word-aligned-prosody.

We prove a variational formula for the Fuglede-Kadison determinant of a self-adjoint matrix semicircle $S_a = a \otimes 1 + \sum_j A_j \otimes s_j$ with deterministic mean $a$. For every real $z$, $\log \Delta(S_a - z) = -1/2 + \inf_b F_z(b)$, where the infimum is over positive definite matrices $b$ such that the map $X \mapsto bXb - \sum_j A_j X A_j$ is positive semidefinite, and $F_z$ is an explicit geodesically convex function. Both sides equal $-\infty$ exactly when $z$ is an atom of the spectral measure. The formula was proposed, without proof, in a recent post of Speicher. In the centered case $a=0$ it gives a new proof of the Mai-Speicher capacity formula, and by hermitization it yields a finite-dimensional variational formula for the logarithmic potential of the Brown measure of an arbitrary matrix-valued semicircular element. The proof identifies the determinant with the value of the Dyson action at its critical point and rewrites this critical-point problem as a saddle problem in three matrix variables. For a spectral parameter $z + i\varepsilon$ in the upper half-plane, eliminating two of the variables gives a geodesically convex minimization whose global minimizer is the positive factor $b_\varepsilon$ in a symmetric unitary factorization of the matrix Cauchy transform. The formula on the real axis follows by letting $\varepsilon \to 0$ in the optimal values, with no compactness assumption on the minimizers. At points where the boundary value of the Cauchy transform is nondegenerate, the scales $b_\varepsilon$ converge and the infimum is attained at their limit; this minimizer lies on the boundary of the feasible set when $z$ is in the support of the spectral measure and in its interior when $z$ is in the resolvent set.

Large language models are increasingly deployed in contexts requiring adherence to ethical and legal norms, yet their alignment with internationally recognized human rights standards remains underexplored. We introduce UDHRBench, a large-scale benchmark for operationalising the evaluation of large language model compliance with the Universal Declaration of Human Rights. The dataset comprises 1,124 human rights confronting questions covering all 30 articles and 4,496 responses from four large language models (ChatGPT, Grok, Gemini, and Fanar), manually annotated by experts for alignment, with high inter-annotator agreement ($\kappa = 0.801$). Our analysis reveals systematic and non-trivial misalignments, showing that violations typically arise through seemingly rational reasoning: appeals to efficiency, risk management, or scientific neutrality, rather than explicit rejection of rights. We further propose an LLM-as-a-Judge framework for automated evaluation using zero-shot and few-shot prompting, achieving 89.8% weighted F1-score in detecting human-rights misalignment, alongside a novel Alignment Leniency Score that quantifies how judge models resolve ambiguous cases. The dataset, annotations, and code will be released as open-source resources (https://sina.birzeit.edu/UDHRBench).

In this paper, we study functional-split selection for an Open radio access network (RAN) deployed as a non-terrestrial network (NTN), in which a low-Earth-orbit (LEO) satellite hosts the radio unit, so that each candidate split (7.2x, 6, 2) places the RAN at a distinct point of the transparent-to-regenerative axis. We capture the space-ground geometry exactly through an instantaneous link plane, which yields closed-form slant range, elevation, delay, and Doppler for an inclined orbit and a rotating Earth. On this geometry we derive the received-SNR density of the elevation-driven LOS/NLOS mixture channel and, through a split-dependent channel state information (CSI) aging mechanism, an uncoded bit-error-rate (BER) law for each split, establishing that what separates the splits is the freshness of the CSI each brings to its adaptation loops: a loop closed on the ground pays the feeder round-trip and incurs an aging-induced error floor. We formulate split selection as a prefer-centralized feasibility problem over reliability, aging, and fronthaul-capacity constraints, and we show that its exact solution is a closed-form region rule in four state coordinates, validated against exhaustive enumeration without a single mismatch. Because this solution is reactive whereas a split change must be initiated ahead of time, we propose a compact Kolmogorov-Arnold network (KAN)-LSTM, sized for an edge xApp/rApp, that predicts the split schedule seconds ahead; we show that it attains high schedule accuracy at a sub-percent BER-violation probability and delivers nearly all of the ground-truth policy's goodput, outperforming naive and reactive baselines.

As agentic AI systems take on increasingly complex and consequential tasks, securing them against prompt injection becomes critical. Existing defenses often rely on detecting or reasoning about injected malicious instructions and can therefore remain vulnerable to adaptive attacks that optimize the injection itself. Diffusion language models (dLLMs), an emerging framework for language generation, offer a new opportunity for security enforcement: by iteratively refining their sequence wide predictions, they enable broader-scope constraint enforcement throughout generation. This paper introduces Policy-Constrained Diffusion Agents (CoDA), a framework that enforces task dependent security policies directly within the denoising process of diffusion language models. At each denoising step, CoDA projects token distributions onto a policy-compliant set, maintaining constraint satisfaction throughout generation. We evaluate CoDA across state-of-the-art diffusion language model families under both static and adaptive prompt-injection attacks. Results demonstrate substantial reductions in attack success rate with competitive task utility and practical inference overhead.

We prove two supercongruence conjectures of Li–Long–Tu concerning truncated very-well-poised ${}_7F_6(1)$ series and Fourier coefficients of modular forms. The proofs are based on a common deformation method. By deforming the original truncated hypergeometric series to suitable terminating series, we are able to apply classical hypergeometric transformations together with Mishev's $W(D_5)$ symmetry. This reduces both problems to congruences for lower-rank hypergeometric sums that can be treated using the $p$-adic methods of Long–Tu–Yui–Zudilin. Although the two cases require different local arithmetic calculations, their global proof structure is the same. The resulting argument gives a unified explanation of these two supercongruences and suggests that the same deformation-and-symmetry method may apply more broadly.

Deuterium metabolic imaging (DMI) measures glucose-derived labeling in vivo, but noisy time courses complicate network-level interpretation. We developed an uncertainty-aware workflow that integrates dynamic DMI data with genome-scale metabolic modeling (GEM) through soft flux constraints. After injection of [6,6'-2H2]glucose, dynamic spectra were acquired from gastrocnemius, soleus, and tibialis anterior muscles of control and high-fat diet (HFD) mice. A hierarchical four-state kinetic model estimated labeling parameters while accounting for shared plasma input, tissue-specific kinetics, voxel-level fluxes, isotope effects, and measurement uncertainty. Because glucose labeling was more reliable than lactate and glutamate/glutamine signals, only two DMI-derived quantities were used as GEM anchors: glucose processing mapped to hexokinase flux, and glucose-derived oxidative entry mapped to mitochondrial pyruvate dehydrogenase flux. Two-sided soft target intervals with weighted penalties defined DMI-compatible feasible regions for each mouse and muscle. Flux variability analysis and sampling assessed changes across reactions and metabolic subsystems. The constraints were compatible with the muscle network and affected feasible activity in glycolysis, lactate metabolism, pyruvate oxidation, the TCA cycle, oxidative phosphorylation, and redox pathways. HFD-associated changes differed by muscle: tibialis anterior and soleus showed reduced glucose-linked feasible activity, whereas gastrocnemius showed mixed changes with preserved or increased TCA and redox activity. This framework connects noninvasive tracer imaging with network-level metabolic inference while avoiding strong claims from poorly identified signals.

The distribution function $F(y)=\Pr(S^2\le y)$ of the sample variance $S^2$ of four independent observations is elementary on its entire support for every polynomial parent density on $[0,1]$ (without loss of generality), and we give it in finite closed form for the uniform, Beta$(2,1)$ and Beta$(2,2)$ parents. The support splits at $y = 1/6$, $2/9$ and $1/4$, with the ceiling at $1/3$, all fixed by geometry: in coordinates aligned with the cube diagonal the event $S^2\le y$ is a ball of radius $\sqrt{3y}$, the cube projects to a rhombic dodecahedron, and these are the levels at which the ball reaches its faces, edges and two kinds of vertices. The divergence theorem reduces every moment of the clipped ball to integrals along circular arcs, so each regime closes in algebraic functions of $\sqrt{y}$ and inverse trigonometric functions. For the uniform parent the only non-obvious constant is $K_g = 12\sqrt2\arctan\sqrt2$, proportional to the mean width of the cuboctahedron; the Beta constants are rational expressions in $\pi$, $\sqrt2$, $\sqrt3$ and $\arctan\sqrt2$, as in the uniform case. At $n = 4$ the normal-theory $\chi^2$ recipe used in acceptance testing misplaces the $99$th percentile of $S^2$ by $50\%$ for the uniform parent. For three observations, polynomial parents also give elementary closed forms (arXiv:2609.25333), but two elementary cases in a row do not guarantee a third, and we make no claim beyond $n = 4$.

We investigate whether a physics foundation model (PFM) pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control. We construct a PFM-based controller by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations and train the policy using proximal policy optimization (PPO). We evaluate the approach on HydroGym's two-dimensional Kolmogorov-flow environment using vorticity observations at \(64\times64\) and \(128\times128\) resolutions and Reynolds numbers \(\mathrm{Re}=100\) and \(200\). Across these settings, we compare the frozen PFM controller against a baseline MLP policy trained with the same PPO framework. The PFM controller achieves consistently higher reward while requiring smaller executed action magnitudes over training, indicating improved control performance with reduced control effort. These results provide initial evidence that representations learned through self-supervised next-frame prediction can be transferred directly to closed-loop fluid flow control. Project page: https://mahindrautela.github.io/morph.

We study a local graph-based interpolation framework for data defined on graph vertices embedded in a metric space. The resulting interpolants are constructed from variational graph splines defined on small neighborhoods, yielding continuous-domain extensions of the graph data. We analyze their behavior through energy estimates, Lipschitz continuity, and stability properties, and compare them with $k$-Nearest Neighbor ($k$NN) interpolation as a natural baseline due to its simplicity and widespread use. Numerical experiments on the manifold of symmetric positive definite matrices illustrate the relative performance of the proposed local interpolation schemes and $k$NN interpolation across varying levels of smoothness and noise.

Canonicalization resolves the rotational and permutation ambiguity of 3D point clouds by selecting a unique orbit representative, maintaining their geometric information while allowing standard architectures, such as Transformers, to operate on them. Existing canonicalizations, however, exhibit discontinuity jumps on molecular configurations and non-trivial invariance errors in popular molecular datasets, which lead to ambiguity in their representation. To bridge this gap, we introduce LexiCan, a canonicalization that is provably invariant under either $O(3)$ or $SO(3)$, empirically invariant to rotations to within $\sim 10^{-6}$ angstroms on the QM9 and QM-sym molecular datasets, and mitigates discontinuity jumps on QM-sym, while running orders of magnitude faster than an existing canonicalization. Finally, non-invariant models perform better on QM9 property prediction and ModelNet40 shape classification with LexiCan than with that canonicalization.

In this paper, we consider joint beamforming and power allocation for a mobile multiuser MIMO integrated sensing and communication (ISAC) network with clutter, residual self-interference, and outdated channel state information, under per-user rate and sensing signal-to-interference-plus-noise ratio (SINR) constraints that must hold on every realization. The design must be recomputed every block, and distant or weak targets can make the sensing constraint unmeetable. We propose a physics-informed unsupervised learning (PI-UnSL) network that corrects the analytical design, meets the power and norm constraints exactly by construction, and is conditioned on closed-form interference statistics, spanning the whole tradeoff in one pass. We derive a closed-form sensing SINR at the interference-aware combiner, yielding a necessary range-radar-cross-section-power condition and a priority-independent analytic violation floor, so the problem is intermittently infeasible. We then show that a dual targeting below the attainable floor has no fixed point, and calibrate the label-free objective against the measured floor. Numerical results confirm the floor and the bounded calibrated dual, and show that PI-UnSL substantially raises per-realization joint quality of service over the closed-form baseline, delivers more rate than time-division ISAC at matched detection over most of the tradeoff, and exceeds the reliability of an uncalibrated alternating-optimization solver at a fraction of its latency. More broadly, the physical knowledge given to the network, not its architecture, makes such problems learnable without labels: five architectures fail alike from scratch and perform alike when started from the closed-form design and conditioned on its interference statistics.

For endomorphisms of the complex projective plane of a given degree, we prove that the existence of a special curve of bounded degree, in the sense of the dynamical Manin–Mumford conjecture, is confined to a proper algebraic subvariety of the parameter space. This confirms a conjecture of DeMarco and Mavraki in dimension two. For general regular polynomial endomorphisms of $\mathbb A^k$, we obtain a uniform dynamical Manin–Mumford bound outside an exceptional hypersurface. These results arise from a common strategy, valid in every dimension and codimension, which reduces such questions to the geometry of exceptional loci in the space of pairs formed by subvarieties and maps. We control these loci by combining arithmetic equidistribution, blender constructions, dynamical directions, monodromy arguments, and degenerations at the boundary of parameter space.

This paper extends the finite-population asymptotic framework of Abadie et al. (2014,2020) to the generalized method of moments (GMM) estimator for moment condition models. Motivating examples include instrumental variable regressions and regression adjustments under randomized controlled trials. We establish consistency and asymptotic normality of the GMM estimator and propose conservative variance estimators. We also study GMM weighting, misspecification, and over-identification testing under finite-population asymptotics. Notably, even though the optimally weighted GMM estimator is infeasible under finite-population asymptotics, the regression adjustment estimator in a randomized controlled trial is shown to be asymptotically equivalent to the optimally weighted GMM estimator. A simulation study and real data application illustrate the usefulness of our GMM theory.

For a $C^*$-algebra $A$ let $\mathcal I(A)$ be the set of all elements $a+b$ with $a,b\in A_+$, $ab=0$ and $\|a\|=\|b\|=1$. We study the algebraic, metric and topological properties of $\mathcal I(A)$. We describe $\mathcal I(A\oplus B)$ and show that $\mathcal I(A/J)\subseteq\pi(\mathcal I(A))$ for the quotient map $\pi:A\to A/J$. For finite-dimensional $A$ we prove $\mathcal I(A)=\operatorname{Sph}^+_A(E(A))$, where $E(A)$ is the set of minimal projections of $A$ and $\operatorname{Sph}^+_A(E)$ is the set of positive norm-one elements at distance one from every element of $E$; we also show that the analogous statement with the minimal projections of the bidual fails in general. When $\mathcal I(A)\neq\varnothing$ the distance from $1$ to $\mathcal I(A)$ is $0$ or $1$, according to whether $A$ has a nontrivial projection. Moreover, $\mathcal I(A)$ is norm compact if and only if $A$ is finite-dimensional, closedness of $\mathcal I(A)$ passes to hereditary subalgebras, $\mathcal I(A)$ is norm closed for every von Neumann algebra, and the extreme points of $\mathcal I(A)$ are exactly its projections. For a compact, locally path connected space $X$ the set $\mathcal I(C(X))$ is closed, whereas $\mathcal I(\ell_c(A))$ fails to be closed when $A$ is unital without nontrivial projections.

Coding agents are increasingly evolving beyond reproducing what a world looks like toward constructing executable worlds that capture how a world works. This shift calls for executable world modeling, which integrates two core capabilities: world understanding, reasoning about the underlying structural, mechanical, and causal principles of a world, and executable realization, translating that understanding into a code-based system whose behavior emerges from physical interactions. However, existing benchmarks provide only fragmented evaluations centered on physical reasoning, visual fidelity, or behavioral correctness, leaving the integration of these capabilities insufficiently assessed. To bridge this gap, we introduce ExeWorldBench, to our knowledge the first benchmark to comprehensively evaluate world understanding and executable realization through code-based 3D world construction. ExeWorldBench comprises three progressively challenging tasks: Mechanism Executability, which evaluates the realization of individual mechanisms from visual observations; Compositional Executability, which extends to multi-stage systems with spatial, mechanical, and causal dependencies; and Intent-Driven Executable World Synthesis, which requires constructing executable worlds from high-level goals and physical requirements. Extensive experiments on frontier models reveal substantial limitations in executable world modeling, offering insights into the development of more physically grounded and causally coherent world construction systems.

Training a classifier to find a rare class of documents, such as hate speech directed at a particular religious group, requires labelled examples that are expensive to obtain when the class makes up only a small fraction of a corpus. Active learning reduces this cost, but it must start from an initial labelled set that contains examples of the target class. Random sampling cannot supply these at reasonable cost, so they must be selected in some other way, such as keyword search, and any such selection biases the initial set towards part of the target class. We evaluate whether active learning can correct this bias. On AG News and Measuring Hate Speech, at a prevalence of around 1%, we compare random sampling with eight active learning strategies, starting from initial sets that cover or omit known subgroups of the target class, and measure recall on the omitted subgroups as well as F1. On AG News, almost every strategy recovers the omitted subgroup. On Measuring Hate Speech, uncertainty-based strategies recover less of the omitted subgroups than random sampling, whereas discriminative active learning recovers 55% of them without a significant loss of F1. Aggregate metrics conceal these differences.