Papers

Academic revision presents a governance problem when legitimate writing objectives conflict. Writing-process and social-science research show that revision is recursive and that wording carries epistemic and disciplinary commitments. Those literatures identify important constraints but do not settle which objective should prevail when concision, outlet form or stylistic variation conflicts with evidence and claim boundaries. This paper models revision as an admissibility problem under ordered constraints. Task-relative invariants, contextual constraints and mutable presentation choices define the admissible space; a claim-preservation contract links evidence and judgement to an authorised claim boundary. Four governance propositions specify preservation, precedence, context and sufficiency. The Academic Writing Filter implements the model by screening candidate revisions; it is not a universal definition or classifier of good academic writing. The contribution is a technology-independent mechanism for changing presentation without silently changing the research argument.

Pediatric high-grade glioma is a dynamically heterogeneous disease in which therapeutic selection pressures, microenvironmental selection and developmental plasticity can reorganize cellular-state structure over time. Here we investigated these adaptive behaviors in glioma dynamics from single-cell ecologies by merging physics-driven artificial intelligence and complex systems theory. Specifically, this study explores canonical residual-based physics-informed neural networks (PINNs), dynamical systems modelling comparators, explainable artificial intelligence (XAI), and Block Decomposition Method (BDM) perturbation analysis to understand glioma cell fate decisions. The primary analyses distinguished longitudinal initial from recurrent H3K27M cells and, within the recurrent specimen set, stem/progenitor-like from differentiated/glial-like annotation-derived states. Across five-fold cross-validation, RD achieved AUC $0.995 \pm 0.005$ and macro-F1 $0.973 \pm 0.016$ for initial–recurrence discrimination, and AUC $0.698 \pm 0.012$ and macro-F1 $0.629 \pm 0.014$ for recurrent-state subtype discrimination. FP achieved AUC $0.931 \pm 0.018$ and $0.665 \pm 0.012$, respectively. Cross-model XAI repeatedly prioritized PTGDS, CHI3L1, IGFBP7, SPARCL1 and NRXN3 in longitudinal progression. BDM perturbation rankings emphasized heat-shock/stress-response and immune-associated network signatures. These findings are candidate computational network biomarkers rather than experimentally established causal signatures. The study provides a reproducible bridge between physics-constrained latent dynamics, interpretable gene attribution, and data-driven algorithmic perturbation landscapes for in silico pattern generation about glioma cell fate plasticity and early recurrence detection.

Intravesical Bacillus Calmette–Guérin (BCG) is an established treatment for non-muscle-invasive bladder cancer (NMIBC), and recent evidence indicates that bladder BCG induces transcriptional and chromatin changes in hematopoietic stem and progenitor cells (HSPCs). However, the joint multi-omic structure of these BCG-associated changes and its potential to define transferable molecular signatures remain less well characterized. This study performed an exploratory integrative analysis of paired single-cell RNA-seq and ATAC-seq data from two NMIBC patients sampled before and after BCG treatment. Following preprocessing and barcode-level integration, 653 HSPCs were analysed using Multi-Omics Factor Analysis (MOFA+) with 2,000 HSPC-specific variable genes and 25,000 variable chromatin-accessibility peaks. Of ten latent factors, Factor~1 showed the strongest association with BCG status ($r=0.495$) and captured variation across both molecular views. RNA weights from Factor~1 were used to derive candidate gene signatures that showed partial consistency across patient-specific models. Cross-context evaluation showed associations with overall survival in TCGA-BLCA and recurrence in GSE199471, while a subset of signature genes showed consistent directional changes in monocytes following BCG vaccination in GSE184241. Together, these findings identify a candidate multi-omic axis associated with BCG exposure and suggest that its derived molecular signatures exhibit context-dependent behaviour across distinct biological and clinical settings.

Clinicians select empiric antibiotics before culture susceptibility results are available. Electronic health record (EHR) models could inform that choice, but most are developed at a single hospital and transport poorly to others. We developed ARMD-Predict using 7.5 million culture-antibiotic observations from four academic medical centers. One set of models estimates susceptibility to individual antibiotics; a second, hierarchical set predicts the infecting organism and then organism-specific resistance phenotypes. Across 23 pooled susceptibility models evaluated in same-period, patient-grouped test partitions, median area under the receiver operating characteristic curve (AUROC) was 0.77 for inpatient urine and 0.70 for inpatient blood cultures; chronological retraining reduced AUROC by approximately 0.04. At an exploratory threshold with 95% positive predictive value, derived and evaluated on the same test observations, the model identified 55% of ceftriaxone-susceptible inpatient urine observations as suitable for narrower therapy and flagged 60% of ceftriaxone-resistant observations for broader coverage. Organism classifiers achieved top-3 accuracy of 51.3-83.3%; phenotype AUROCs were conditional on the observed organism. Research applications are available at https://armd-predict.stanford.edu. Independent calibration, threshold and end-to-end prospective validation are required before clinical use.

The CIDOC CRM family is not only a schema for museum collections. Its extensions formalise the apparatus through which research knowledge is produced and justified: CRMsci models scientific observation and measurement, CRMdig the provenance of digital processes, CRMinf inference and belief. Together they constitute a schema for research data, and the obstacle to their adoption is documentary rather than theoretical: four normative documents, four code conventions, and eighty-nine typed links crossing document boundaries. This paper presents the CIDOC CRM Periodic Table, a single-page browser rendering 131 classes and 480 property entries from CIDOC CRM 7.1.3, CRMsci 3.2, CRMdig 5.0 and CRMinf 1.2.1 as one navigable surface, with two inference facilities: a one-step triple builder admitting only the class-property combinations licensed by declared domains, ranges and the subclass closure, and a multi-step path finder enumerating property chains between two classes. Because all loaded models are merged into one code-keyed dictionary before the hierarchy closures are computed, both resolve chains that cross model boundaries; we document the addition of CRMsci and the three cross-model tests it made possible, and report preliminary uptake signals from 56 months of analytics, with the reading they support.

We study equality between metric dimension and the maximum eigenvalue multiplicity of the Laplacian and signless Laplacian matrices. These quantities are not ordered in general. Using the standard decomposition associated with twin classes, we separate forced multiplicities from quotient-spectrum contributions. We give complete equality classifications for complete multipartite graphs and core–satellite graphs, and enumerate the multipartite equality graphs by order. For graphs formed by attaching at least two leaves to every vertex of a connected core, the metric dimension and the multiplicity of the eigenvalue $ 1 $ are known; we show that this multiplicity is maximal for both matrices, and uniquely maximal except for $ P_3 $. We enumerate this core–leaf family up to isomorphism and obtain a uniform asymptotic formula by order and metric dimension, together with the quadratic exponential growth rate $ 1/18 $. An exact census of connected graphs of orders two through seven identifies the first separating examples and examples without twins. Finally, for every odd $ r \in \mathbb{Z}_{\geq 3} $, we study $ \Theta_{2, 2, r} $ and determine both maximum multiplicities: the two equality properties alternate with $ r $ modulo four, producing infinite separating families in both directions.

Cell fate plasticity dynamics in glioma ecosystems is usually inferred from static single-cell snapshots, leaving a gap between manifold geometry, predictive modelling, and mechanistic intervention ranking. We developed scCTM, a complexity theory and machine learning framework that combines the Sakana AI Continuous Thought Machine (CTM) with autoencoding, a continuous actor-critic policy over synchronization-derived latent states for predicting single-cell fate dynamics. We also incorporated integrated-gradient and decoder-weight explainability, network science, empirical Waddington-like landscape (attractor) reconstruction, and post-hoc Block Decomposition Method (BDM) perturbation analysis. The complexity framework was evaluated in two malignant cell secondary analyses: GSE210567 stem-like versus differentiated H3K27M cells (18,490 cells) and longitudinal H3K27M initial versus recurrent disease trajectory (20,000 cells) from Sussman et al. (2026) as a ML binary classification problem. CTM-AE achieved AUROC values of $0.99$ in both datasets. CTM-RL preserved classification almost exactly but did not improve reconstruction. Out-of-fold CTM-RL latent states produced potential basins across PCA, UMAP, and PHATE embeddings. BDM edge perturbation analysis further identified recurrent high-impact network interactions, including epigenetic/chromatin-associated signatures involving ARID1B and developmental or neuronal-state genes such as AUTS2, CTNND2, DPP6, NRXN1, and CADM2. These in silico findings support CTM synchronization as an interpretable latent-state representation and predictive forecasting of cell fate dynamics, as well as BDM perturbation signatures as a complementary in silico intervention ranking layer for systems medicine.

Fake accounts continue to undermine online platforms, yet it remains unclear whether multimodal learning offers meaningful improvements over strong metadata baselines or graph-based approaches. In this work, we study bot detection by integrating textual, visual, and account metadata signals on the TwiBot-22 benchmark using a subsample of 30,000 users. We propose a multimodal framework combining pretrained textual (XLM-RoBERTa) and visual (CLIP) embeddings with structured account-level features such as follower counts, posting frequency, and account age, and evaluate multiple modality combinations using CatBoost alongside a Relational Graph Convolutional Network (R-GCN). Results show that metadata alone is highly predictive, while multimodal fusion yields only marginal and largely statistically insignificant gains. The graph-based model underperforms classical variants under the subsampled graph conditions of this study. Overall, our findings suggest that under practical constraints, feature quality and metadata richness matter more than fusion complexity.

We introduce SpinDoctor, a method for discovering innocuous prompts for text-to-image models that result in images with a chosen target bias, while retaining the quality of the images and prompts. These prompts present a risk for user manipulation, in that a user who is given these seemingly unbiased prompts might be willing to use them and would receive biased images in return. Our method is flexible: it uses models in a black-box way only and the target image bias can easily be changed, and so our method can be applied with various motivations and in various scenarios. Our method shows some transferability between models-we saw the same bias emerge in 78.6% of cases-such that a victim who uses a prompt generated via our method using one model still likely receives a biased image from another model. In our experiments, a subset of which we corroborated with human evaluation, we were able to find an innocuous prompt that moved generated images in the direction of the desired bias in all but two of 304 experiments, with an average improvement of 34.8% and 33.5% on two open-source text-to-image models.

Pure gravity quantum gravity (pure gravity QG) is non-renormalizable at two and higher loop level. One of the main characteristics of objects occurring in QG is their Lorentz covariance. QG necessitates the analysis of a collection of Lorentz covariant terms of higher and higher order, which is not feasible using renormailization. This paper describes how the regularization technique known as covariant spectral regularization (CSR) can be used to analyze Lorentz covariant 4-tensor valued measures on Minkowski space. The graviton vacuum polarization tensor is cast as such a measure and CSR is used to obtain a well defined and finite function representing this tensor. This is then used to compute the Feynman amplitudes for examples of one-loop, two-loop and $n$-loop graviton-graviton scattering in pure gravity QG. The CSR method results in functions (densities) representing divergent Feynman integrals without requiring renormalization or counterterms. Therefore it can be used to analyze arbitrarily complicated multiloop QG Feynman diagrams without being crippled by a proliferation of counterterms, as is classical QG.

Tabular data are prevalent across diverse domains such as healthcare and finance. Zero-shot tabular learning aims to make predictions without labeled data. However, existing LLM-based approaches rely on row-wise prompting, resulting in high inference cost and limited use of inter-row dependencies. In this work, we propose TABHGR+, an efficient relation-aware zero-shot framework for tabular data that leverages LLM-generated rules to label and group rows. Specifically, based on column and task descriptions, we use LLMs to generate rules that assign weak labels to all rows. To refine these noisy weak labels, we construct a hypergraph by grouping semantically related rows using LLM-generated rules and perform hypergraph-based label propagation. Lastly, we further enhance the LLM-generated hypergraph for propagation, which is potentially sub-optimal, by assigning label-adaptive weights to hyperedges. By requiring only a constant number of LLM calls independent of dataset size, TABHGR+ substantially reduces inference cost while achieving higher classification accuracy than zero-shot and strong few-shot baselines.

Generative semantic communication (SemCom) enables low-bandwidth image transmission by reconstructing images from semantic descriptions. However, text-only schemes often suffer from poor structural fidelity due to the stochastic nature of generative models, while still requiring high transmission payload and inference latency. This letter proposes a dual-information-flow SemCom framework based on Flow Matching. At the transmitter, the most semantically matched prompt is selected from multiple candidate descriptions, while an ultra-low-dimensional structural residual velocity vector is extracted from the inversion trajectory of the original image. At the receiver, a Time-Aware Recursive Residual Injection (TARRI) network progressively releases structural corrections along the denoising trajectory using the transmitted residual vector as structural memory. The proposed framework transmits only prompt embedding and a compact residual vector, achieving robust high-fidelity image reconstruction under extremely low payload. Experimental results demonstrate that the proposed framework significantly improves both structural fidelity and perceptual quality over existing text-driven semantic communication schemes.

We investigate sorted mutability, $\zeta_S$, as an information-based quantity with an explicit entropic character. We show that $\zeta_S$ is directly proportional to the diversity of a data sequence and can therefore be expressed in terms of Shannon entropies, establishing a connection between compression-based measures and conventional information theory. In contrast to regular mutability, which preserves the sequential ordering of the data, sorted mutability removes this ordering and provides a static characterization of the distribution of observed values. We illustrate these properties in two complementary settings: the two-dimensional ferromagnetic Q-clock model and wind-power production data. For the Q-clock model, sorted mutability and diversity display the same temperature dependence, consistent with their analytical relation, while conventional thermodynamic observables provide an independent reference. In the case of wind power, we report monthly results for sorted mutability and diversity, showing proportional time evolutions. These results support sorted mutability as a useful, easy-to-calculate entropic functional for analyzing both equilibrium and non-equilibrium data sets.

Natural supercavitation behind conical cavitators generates a vapor-filled envelope that, when sustained over the full body of a high-speed underwater vehicles, reduces hydrodynamic skin-friction drag and enables performance levels unattainable in fully wetted flow. Accurate prediction of maximum cavity length and maximum cavity radius and local cavity profile as functions of cavitation number and cone half-angle is essential for both the static design and the real-time shape management of super-cavitating torpedo cavitators. Classical analytical models provide computationally inexpensive predictions but exhibit systematic disagreements in the practically important regime of moderate cavitation number and large angle, where slender-body assumptions begin to break down. Existing data-driven machine learning approaches offer higher accuracy but are constrained by the prohibitive cost of multiphase computational fluid dynamics (CFD) sweeps over the full design space. This study proposes a physics-guided multi-fidelity surrogate framework based on Extended Hierarchical Kriging (PG-EHK) that addresses this challenge by fusing the multiple competing analytical cavity formulas as non-level low-fidelity (LF) trend functions corrected by a sparse set of high-fidelity (HF) CFD data. It simultaneously incorporates the analytical models regardless of their local fidelity ordering, using Bayesian-estimated scaling factors to construct the trend function as physical baseline. The resulting surrogate maps operational condition inputs to cavity geometry responses using fewer than 20 high-fidelity CFD evaluations. Cross-validation on five independent hold-out CFD cases demonstrates that the proposed PG-EHK surrogate achieves 61% reduction in prediction error compared to the best-performing individual analytical approach.

The discriminant of a square matrix is defined as a discriminant of its characteristic polynomial. In this paper we provide a description of linear maps preserving the matrix discriminant assuming that the ground field is large enough. Our description generalizes the known results to the case where the field may have a finite cardinality and its characteristic may divide the size of considered matrices. To obtain this description, we extend the approach used in our previous work on the subject and, in addition to that, introduce new invariants for the action of all bijective linear maps preserving a given polynomial, which are on independent interest and could be applied to other problems in the theory of linear preservers.

Rapid advances in AI have opened a new era for physics, enabling unprecedented capabilities in research and discovery. However, these advances also bring challenges in verifying, trusting, and reusing the results they so rapidly produce. Formalization is a necessary part of the solution to these challenges. In this paper, as well as giving an overview of the role of AI and formalization in physics, we make the case that: (1) formalization is an essential layer for AI-driven discoveries in both computational and theoretical physics; (2) AI is lowering the barrier to, and increasing the efficiency of, formalization in physics, though it remains weaker at choosing definitions and designing libraries than at writing proofs; (3) the speed AI brings to formalization in physics currently comes at the cost of trust, credit, and community; (4) shared, community-reviewed formal libraries such as Physlib should be central in making progress in this field, both as a trusted, reusable foundation for physics results and as the environment in which AI systems can reason about physics; (5) formalizing physics raises challenges beyond those in mathematics, most importantly that a checked proof does not establish that its definitions faithfully capture the intended physics. We also give our perspectives on near-term and long-term directions in these areas.

Nearby compact gamma-ray sources can move appreciably during the Fermi-LAT mission and thus evade searches that assume a stationary sky. Compact dark matter halos, dark matter spikes around primordial black holes (PBH), and evaporating PBH provide potential examples. We perform a novel all-sky search for steady point sources moving at 0.25 deg/yr-0.8deg/yr in ten years of 1-100 GeV Fermi-LAT data. For a transverse speed of 200 km/s, this angular range probes distances of roughly $3.0\times10^3$ AU to $9.7\times10^3$ AU. We find 577 candidate tracks, consistent with $533\pm27.0$ tracks in time-scrambled skies. We place a model-independent 90% upper limit of 80.8 recovered signal tracks. At peak calibrated sensitivity, this corresponds to fewer than 123 steady, full-sky sources with an incident $E^{-2}$ photon spectrum. We give the calibrated detection efficiency of the search to steady point sources and use it to derive illustrative constraints on both evaporating PBHs and PBHs surrounded by annihilating dark matter halos.

acousticHelmholtzFoam is an OpenFOAM application that computes time-harmonic acoustic pressure fields in heterogeneous gas-liquid media on unstructured polyhedral meshes. The complex pressure is stored as real and imaginary volume fields, the material coefficients are constructed from a volume-of-fluid phase fraction with geometric face-fraction averaging, and open boundaries are truncated by Cartesian perfectly matched layers (PMLs) whose damping tensor is generated by the companion utility setPMLFields. The two coupled real-valued equations are discretized with the cell-centred finite-volume operators of OpenFOAM and assembled explicitly, including processor couplings and boundary contributions, into a distributed PETSc matrix that is solved by default with the MUMPS sparse direct solver. The solver writes pressure amplitude, complex velocity, acoustic radiation pressure and time-averaged momentum flux for acoustic-force evaluation. This paper documents the implemented equations, the case interface, the assembly and solution algorithm, the build procedure and the test infrastructure. A layered gas-liquid-PML case with an analytical solution serves as an end-to-end regression: on 8000 cells the whole-domain relative complex-pressure error is $1.197\times10^{-3}$, and serial and MPI solutions on up to eight ranks agree to within $10^{-12}$ in relative $L_2$ norm. A single-axis acoustic-levitator height sweep with constant-volume spheroidal drops demonstrates the two-phase material input and the force output, and strong- and problem-size-scaling measurements characterize the direct-solver workflow. The numerical formulation and its verification are presented in a companion paper (arXiv:2610.01593).

A speech synthesizer produces a detailed waveform, but a listener need not hear every detail. Strong sounds can mask weaker neighbors, creating context-dependent "blind spots" in hearing. Could neural text-to-speech (TTS) spend less computation on those details? We investigate a first step: how the placement of spectral degradation affects completed speech from Piper and Kokoro. At matched time-frequency bin-removal budgets, a simple low-energy-first policy achieves higher mean wideband PESQ than random deletion and the tested psychoacoustic masking criteria. At 50% removal in the spreading-matrix comparison, energy, masking, and random policies score 4.46, 3.60, and 1.19 on Piper, and 3.42, 2.10, and 1.22 on Kokoro. Spectrograms and masking maps expose where these perturbations fall and why a model's below-threshold regions cannot automatically be treated as inaudible. Calibration diagnostics show substantial threshold sensitivity, while a small single-listener pilot establishes no transparent removal budget. CPU profiles identify waveform decoding as the main measured kernel cost, but a tested dynamic-INT8 Kokoro decoder runs slower than FP32 on both CPUs. The results establish energy ranking as a strong oracle baseline and motivate testing perceptual allocation inside a decoder. They do not yet demonstrate saved computation: the decisions here use already synthesized audio, and quality metrics are evaluated at 16 kHz. We release scripts, results, audio examples, and a listening-study instrument.

For every integer $k\ge1$, we prove that each nonempty bounded set in real $\ell_1^{4k+1}$ has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: $J(\ell_1^5)=3/4$. If a Hadamard matrix of order $4k$ exists, then $J(\ell_1^{4k-1})=J(\ell_1^{4k})=J(\ell_1^{4k+1})=(4k-1)/(4k)$. The upper bound for every $k\ge1$ has been formalized in Lean.

Program evaluations routinely find larger effects of investment in low-skill children, while structural models of skill formation typically find that skill and investment are complements. I reconcile these findings by introducing the Average Marginal Return (AMR), which averages the marginal return to an input over the distribution of other inputs, providing a structural analogue to the average treatment effects estimated in program evaluations. The AMR reveals why input scales and distributions matter for the economic interpretation of structural estimates, why reduced-form interaction coefficients need not identify technological complementarity, and why dynamic complementarity can be difficult to detect in reduced-form work. I estimate AMRs to parental investment using a dynamic factor model of cognitive and noncognitive skill formation for ages 5-14 in the Children of the NLSY79. I accommodate binary and Likert measures using ordered probits, showing that treating them as continuous substantially biases estimates, and introduce effective factors to extend the scale-invariant normalization of Freyberger (2026) to models with multiple skills per period. Investment in early childhood generates larger long-run gains in cognitive skill than investment at later ages. Although skill and investment are complements, the AMR to early investment is initially flat across skill levels but becomes sharply decreasing in initial skill over time. By ages 13-14, children at the 10th percentile of early cognitive skill gain roughly twice as much from early investment as children at the 90th.

We study the game chromatic number of complete multipartite graphs whose parts are either singletons or are of size at least four. Building on the work of PawełObszarski et al., we give a formula in terms of the ordered part sizes, and the number of singleton parts.

Sensing-aided beam prediction can reduce the beam-training overhead of millimeter-wave (mmWave) systems by leveraging environmental information from complementary modalities such as vision and position. However, the resulting sensing and inference pipeline can be energy-intensive, motivating the use of energy-efficient spiking neural networks (SNNs) as an alternative to conventional artificial neural networks (ANNs). In this work, we develop SNN architectures for beam prediction and systematically compare them with ANNs using position-only, vision-only, and multimodal inputs. Our results show that compact ANNs consistently outperform SNNs for position-only sensing. In contrast, for vision and multimodal sensing, SNNs achieve higher accuracy than ANNs at similar energy costs and require up to an order of magnitude less energy at a comparable accuracy. For example, the multimodal SNN achieves 58.08% top-1 accuracy, outperforming the closest-energy ANN by 18.11 percentage points. We further show that SNN accuracy is limited by the binary communication between layers rather than by model size. These results demonstrate the potential of SNNs for energy-efficient sensing-aided beam prediction while highlighting their accuracy limitation.

We investigate intra-chain exciton energy transfer (EET) in a conjugated polymer using a reduced three-level donor-acceptor model that separates vertical excitations from vibrationally relaxed states. Population dynamics are obtained with the hierarchical equations of motion (HEOM), enabling a non-Markovian treatment of system-bath (S-B) interactions. Case studies on donor-acceptor (D-A) pairs with small and large energy gaps reveal competition among coherent hopping, vibrational relaxation, and Förster resonance energy transfer (FRET). Varying the hopping and the S-B relaxation rate highlights roles of exciton transfer, thermal relaxation, and dipole-mediated coupling. The results show that energy gap, hopping, and relaxation jointly control intrachain EET.

Reinforcement Learning (RL) has enabled legged robots to perform a range of skills in single-task settings. However, applications such as farm robotics or space exploration require diverse skills such as locomotion, digging, or close-range surveying. Training an end-to-end policy to address this problem remains difficult due to challenges such as sample inefficiency and gradient conflict between tasks in multi-task learning. We propose a three-stage method that trains a single policy to perform distinct tasks such as walking, digging, and hopping, and compose them into novel behaviors such as crawling. First, multiple teacher policies are trained using RL on narrowly defined tasks. Then, two additional stages train a student policy with a multi-teacher distillation setup that uses a combined RL and Imitation Learning (IL) objective under an adversarial task selection process that focuses training on the worst-performing task. With this method, we train a student policy that performs 22 tasks using 8 teachers. Evaluations show our method preserves motion quality and tracks commands more accurately than PPO and distill-then-finetune baselines, and in some cases generalizes to new tasks without explicit training. Finally, we demonstrate real-world robustness by deploying the resulting policy on a Unitree B1 quadruped. Video: https://youtu.be/V9yX04EBcFA

Steinke and Zakynthinou(2020) introduces the Conditional Mutual Information (CMI) framework of analyzing the information complexity of learning algorithms based on algorithm-dependent information-theoretic quantities. We study one of these quantities, the evaluated Conditional Mutual Information (eCMI). It has been an interesting question whether the optimal PAC guarantee for VC classes can be recovered from the algorithm-dependent analyses via CMI. And we show that it is possible to recover this guarantee by constructing a learning algorithm whose eCMI is of order O(d) in the realizable case, where d is the VC-dimension of the concept class. Specially, our algorithm is a randomized Majority-of-5 base learners with optimal in-expectation generalization guarantee.

We prove that a random 3-SAT formula with $n$ variables and $\lfloor 4.268n\rfloor$ clauses is unsatisfiable with high probability. The satisfiability threshold has attracted considerable attention: successive upper bounds reached 4.4898 in the work of Díaz, Kirousis, Mitsche, and Pérez-Giménez, while the cavity method predicts a value near 4.267. Our bound brings the rigorous upper estimate close to this prediction. The proof builds on earlier interpolation methods, including the energetic approach of Achlioptas and Menchaca-Méndez. We study the smallest number of clauses that any assignment must violate, comparing the random formula with a simpler system of constraints on individual variables. This comparison reduces the bound to a finite calculation, which we verify using exact rational arithmetic. The proof is formalized in Lean 4.

Emerging edge applications must sense their environment and process data within tight latency budgets. Full-duplex (FD) integrated sensing, communication, and computing (ISCC) supports these functions concurrently, but radar probing interferes with uplink reception while user transmissions degrade target estimation. These coupled effects call for joint sensing and offloading decisions. We investigate a FD massive multiple-input multiple-output (mMIMO) ISCC network in which users partially offload tasks to an edge server while an access point probes a target. For zero-forcing uplink reception with imperfect channel estimates, we derive a tractable rate bound and target-angle Cramer-Rao lower bounds (CRLBs) under the stated interference and beam-alignment assumptions. We then jointly optimize offloading fractions, user and radar transmit powers, and edge computing resources to minimize average end-to-end task latency subject to sensing-accuracy, communication-rate, energy, deadline, and resource constraints. A successive convex approximation algorithm is developed to efficiently address the resulting nonconvex problem. The analysis shows that larger arrays improve sensing and uplink performance, but residual radar interference creates a finite rate ceiling when user powers scale down with array size. Simulation results show joint allocation reduces radar transmit power by approximately 86% relative to equal communication-user power at a -40 dB CRLB threshold and lowers latency compared with fixed-allocation and half-duplex schemes.

Public leaderboards for AI models are read continuously, and attackers can see every published standing. Vote rigging, selective disclosure of private variants, and benchmark contamination can each move a ranking. Existing guarantees assume genuine records or bound the corruption per step, which an attacker who corrupts in bursts evades. We introduce the certified corruption budget, a tolerance $\widehat{B}_t$ computed after $t$ records and published with each pairwise claim. With probability at least $1-\alpha$, simultaneously at all times, the claim is correct or more than $\widehat{B}_t$ records were corrupted. It holds against attackers who watch every certificate, with no bound on their budget. Forged records and records altered once seen require different certificates: the certificate for forgeries fails, with probability approaching one, against an attacker who flips votes it has seen, while one that charges roughly twice as much per record remains valid, with constant bets even against attackers who see the future, and no smaller charge is valid at every level. The certified budget grows nearly as fast as any valid method allows: with a win fraction $\frac{1}{2}+\delta$, each new record adds close to $2\delta$ to the number of forged records the claim can withstand ($\delta$ flipped). Publishing the best of $V$ private variants costs only an amount growing like $\log V$. In replays on 1.8 million Chatbot Arena votes, a few hundred rigged votes make standard confidence intervals certify false orderings, while ours stays valid. On real votes, our certificate shows that clearly separated models withstand about 2,000 forged votes.

Dijkstra's algorithm is traditionally classified as a greedy algorithm. We argue that this classification misrepresents the mechanism by which the algorithm determines shortest paths. We present a direct global-to-local proof of correctness. At each iteration, the algorithm identifies a shortest path over the entire set of paths whose endpoints remain unsolved. This global minimum is necessarily a shortest path to its own endpoint. More fundamentally, the algorithm uses already determined shortest paths to establish one additional shortest path at each iteration. We identify this progression as dynamic programming. A three-step exclusion proof shows how the full path space is reduced to frontier candidates, how relaxation removes inferior alternatives, and why minimum extraction yields the global minimum. The choice is thus determined by a global comparison, not by an optimistic local greedy choice. We conclude that the algorithm is more accurately characterized by dynamic programming and deterministic path exclusion than by the traditional greedy classification.