Papers

External verification can correct individual outputs while leaving a self-reinforcing population in the basin of a wrong consensus. We study how the timing and addressing of a fixed verification budget affect recovery in an asynchronous binary register. For a general nonlinear response, we derive the minimum fuel required to cross a basin boundary under a peak verification constraint. For a finite population, an exact birth–death calculation gives the probability of subsequent wrong consensus after a pulse. Our main asymptotic result identifies the critical budget window: a leading term $N\log(x_0/b)$ and a correction of order $\sqrt N$, with separate variance contributions from repeated verification targets and autonomous amplification after verification stops. The distinction is substantial: with 16 majority-updated slots and 14 initially wrong, 9 random checks cross the mean-field budget threshold, whereas 23 are required for 95% eventual recovery in the exact model. A prospectively specified experiment records 13,392 language-model responses, including calibration and 108 held-out trajectories. Calibration produces different fitted response regimes, but all four adjusted schedule-comparison intervals include zero. A distributional audit also finds that modest mean-prediction error can conceal a large underestimate of terminal consensus occupancy. The results support risk-calibrated reset scheduling under a specified update contract, while explicitly separating it from distinct-target checking and unrestricted evidence broadcast.

Quantum compiler assurance requires a semantic relation that matches the intended use and observations that can expose violations at the delivered interface. This critical integrative survey compares verified transformations, equivalence checking, differential and metamorphic testing, property-based testing, and evidence for assurance across revisions. A source catalogue and focused extraction matrix distinguish formal guarantees, reported empirical findings, analytical deductions, and proposed practice. A recorded coverage update and source-level selection decisions make the review auditable within its declared scope. Four documented failure cases connect conditional applicability, parameter association, termination, and phase conventions to method selection. A worked example involving layout metadata, parameter bindings, and ancillary qubits demonstrates why validating a circuit under a reconstructed interpretation can leave the delivered interface unchecked. An illustrative revision scenario then separates fault detection from change attribution. The resulting guidance specifies applicability, complementary observations, and treatment of inconclusive outcomes. Published bug counts, mutation results, and processing benchmarks support different claims and do not establish a common effectiveness ranking. The proposed regression architecture remains unevaluated as a complete system; its practical value requires controlled comparisons on independently adjudicated compiler-change events.

The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, $q$-para-Racah and para-Bannai–Ito polynomials followed, obtained through singular truncations of families of the Askey scheme and used in turn to design spin chains. All are orthogonal on bi-lattices; the prefix goes back to the para-Krawtchouk case, whose spectrum is that of the parabose oscillator. The representations that these polynomials provide of the corresponding algebras — Hahn, Racah, $q$-Racah, Bannai–Ito and complementary Bannai–Ito — are shown to be reducible. Each decomposes into a direct sum of two irreducible modules of the same algebra, one attached to each of the two interlaced sub-lattices, and the parameters of the submodules are given. The para polynomials are thereby expressed in terms of the classical polynomials that the submodules carry, and the pairing $\lambda_n=\lambda_{N-n}$ of their eigenvalues is accounted for; the three features of the bi-lattice setting on which the reduction rests are identified. The properties of the para families are then presented in a unified way in the light of this decomposition, together with the constructions through which these families arise and the settings in which they have been put to use.

Exact periodic solutions of the unforced incompressible Navier-Stokes equations require the convective field to be a pure gradient, absorbed into the pressure; for the cyclic trigonometric families studied previously this occurs only at isolated phases and, over the range so far classified, only at n = 3 and 4. The forced problem, we show, admits an exact construction for every phase vector and every n >= 3. For an n-parameter family of two-term cyclic fields, solenoidal and a Laplacian eigenfunction, the transverse part U^0 of its convective field serves as the body force, giving a closed-form solution with velocity, pressure and force explicit. We prove closed forms for the pressure and for both magnitudes, in every dimension and with no upper bound on n: the forcing is never trivial, and the L^2 magnitude of U^0 stands to that of the whole convective field in the constant ratio 2*sqrt(2)/3, whatever the dimension, phase or units. The forcing does no net work, so the kinetic energy decays purely viscously at arbitrary Reynolds number, giving an exact benchmark in any dimension. A numerical study of vorticity concentration at zero applied work uses it as a reference, and shows that apparent saturation can be a resolution artefact.

Stochastic quantization formulates $d$-dimensional Euclidean QFT as the equilibrium limit of a $(d+1)$-dimensional Langevin system. Using the supersymmetric formulation of stochastic systems, we apply techniques from Morse theory to study Langevin dynamics. We interpret stochastic quantization as the absolutization of a relative QFT by a bulk cohomological topological Equilibrium TFT ("EqmTFT"), and relate its enriched Neumann boundary data to the $d$-dimensional BV/BRST complex. Analytic continuation reveals connections to the A-model and non-relativistic and Carrollian limits.

Smoothed particle hydrodynamics (SPH) is well suited to large-deformation fluid problems, and the growing use of automatic differentiation in engineering applications has motivated interest in differentiable SPH solvers. In this study, a composable differentiable SPH framework, CraftSPH, has been developed. In CraftSPH, major computational operations are implemented as independent modules that users can combine to construct solvers for different purposes. This design supports high-accuracy discretization and both explicit and implicit computation within a common framework, while allowing individual components to be maintained and extended. Selected numerical operations also support automatic differentiation (AD) for physical-parameter estimation and potential coupling with deep learning models. These capabilities were demonstrated through forward and inverse analyses. Forward analyses using an implicit SPH scheme with high-accuracy discretization showed good agreement with analytical and reference solutions for Poiseuille flow and a rising bubble, while capturing the key experimental trends in two- and three-dimensional dam-break problems. In inverse analyses, explicit and implicit SPH schemes were used to estimate kinematic viscosity in Taylor-Green vortex flow and Reynolds number in lid-driven cavity flow. The results also showed that the choice of operations included in the computational graph affects the computed gradients. Together, these findings demonstrate that CraftSPH enables users to assemble problem-specific solvers for forward and inverse analyses within a common framework.

FireworksWeb is a web-based event display utilizing a C++ ROOT-Eve backend with SAPUI5 frontend for interactive 3D visualization of particle physics events directly in the browser. Building upon ROOT-Eve and RenderCore, it eliminates local software installation while maintaining professional-grade event display capabilities. FireworksWeb is currently deployed for live event monitoring in the CMS control room, demonstrating its reliability for real-time data visualization in production environments. The CMS experiment has made a large amount of collision datasets publicly available through the CERN Open Data portal, which are the valuable resources for education, outreach, and research. We have extended FireworksWeb to enable visualization of these open datasets, making particle physics data accessible to diverse audiences without requiring local software installation. Our prototype implementation includes standalone cameras, event filters, configurable collection settings, and projection controls with fish-eye distortion for cylindrical geometries. The web architecture communicating via CGI enables dataset queries and filtered event selection based on physics criteria. We demonstrate the prototype with CMS Open Data events, discuss the technical architecture, and outline applications for education, public outreach, and exploratory physics analysis.

The representation number of a graph is the least positive integer $k$ for which its vertices can be arranged in a word, each occurring $k$ times, so that two distinct letters alternate precisely when the corresponding vertices are adjacent. We prove that every bipartite graph on $N\ge9$ vertices has representation number at most $\lceil N/4\rceil$. Together with the known representation number of crown graphs, this settles the conjecture that crowns maximise the representation number among bipartite graphs of the same order. The proof develops a construction of Mozhui and Krishna by reducing the choice of a representing word to an ordering problem for neighbourhoods. We characterise the obstructions to this ordering and use probability estimates to exclude them for all sufficiently large balanced bipartitions. Two finite assertions complete the argument, each established by a checked Boolean unsatisfiability certificate. A refinement of the ordering argument treats the remaining odd part sizes directly. The main theorem and the crown-extremality corollary, including the finite certificate arguments, have also been formalised and verified in Lean 4.

Mutation testing evaluates test-suite adequacy by injecting synthetic faults into program code. However, traditional rule-based tools often generate large numbers of trivial, redundant, or equivalent mutants that limit their practical use for identifying gaps in a test suite. While recent large language model (LLM)-based approaches generate more realistic faults, most remain test-blind: The model sees only the source code and cannot reason about what existing tests already cover. We propose test-aware mutant generation, in which an LLM receives the problem statement, canonical solution and base tests in a single prompt, and must generate a nontrivial mutant that passes the base unit tests. We evaluate this approach across a set of five LLMs – Gemini 3.1 Pro, Gemini 3 Flash, GPT 5.1 Codex Mini, GPT 4.1 Mini, Qwen3-32B – on the HumanEval and MBPP benchmarks. The extended EvalPlus test suites serve as an automated oracle to verify whether surviving mutants represent genuine bugs. Test-aware prompting yields verified fault rates of 87.7% (HumanEval) and 79.1% (MBPP), meaning these mutants pass all base tests but are caught by the oracle. This vastly outperforms the matched test-blind prompting (which yields only 12.2% and 23.0%, respectively) and the traditional rule-based tool mutmut (4.4% and 5.7%). While fault subtlety (the fraction of extended tests a mutant fails) remains comparable across all three methods, test-awareness minimizes the computational cost per verified fault, compared to test-blind prompting. Exposing an LLM to existing unit tests shifts mutant generation from untargeted bug injection toward effective discovery of weaknesses in an existing test suite. Our work establishes a concrete foundation for future research to scale test-aware mutant generation to production-level environments.

We establish matching polynomial query bounds for low-rank approximation from exact matrix–vector products. Given an unknown matrix $A\in\mathbb{R}^{m\times n}$, at each step a randomized algorithm chooses either $v\in\mathbb{R}^n$ and receives $Av$, or $u\in\mathbb{R}^m$ and receives $A^\top u$. The choice may depend measurably on all previous queries and replies and on the algorithm's private randomness; each vector product costs one query. The output is a rank-$k$ right projector with Schatten-$p$ residual at most $1+\varepsilon$ times optimal. Write $N=\min\{m,n\}$ and let $Q_p^*$ denote the worst-case query budget for success probability $2/3$ on every input. For every $1\le k<N$ and sufficiently small $\varepsilon$, our lower bounds, combined with existing Krylov upper bounds, give $Q_p^*=\widetilde{\Theta}\!\left(\min\{N,k\min\{p^{1/6}\varepsilon^{-1/3},\varepsilon^{-1/2}\}\}\right)$ $(2\le p<\infty)$, $Q_\infty^*=\widetilde{\Theta}\!\left(\min\{N,k\varepsilon^{-1/2}\}\right)$. These bounds have universal constants and allow $p$ to vary with the problem parameters, identifying the transition at $p\varepsilon\asymp1$. A complementary result for each fixed $1\le p<2$ gives $\widetilde{\Theta}_p(\min\{N,k\varepsilon^{-1/3}\})$, with constants and an accuracy threshold that may depend on $p$. Together, the results recover this fixed-norm rate for every fixed finite $p$, supplying the multiplicative rank dependence missing from previous lower bounds. Tildes suppress logarithmic factors. The proof extends adaptive Wishart deferred decisions to a rectangular factor with a $k$-dimensional nullspace. Posterior overlap gives a short fixed-norm argument, while persistence of small compression eigenvalues controls growing $p$ and the spectral endpoint. Exact range recovery handles target costs of order $k$; the Wishart family covers the remaining regimes.

Handclaps provide an equipment-free excitation for room acoustics, but their unknown and variable source waveform makes room impulse response (RIR) estimation challenging. In this work, we investigate whether RIRs can be estimated directly from handclaps. To this end, we introduce an anechoic handclap dataset containing 2,540 claps from 17 participants, designed to capture variability across natural claps and different hand configurations. We first establish the performance attainable when the excitation clap is known using regularized deconvolution, and show that approximating the unknown excitation by windowing the direct sound from the reverberant recording is insufficient. To estimate the RIR without a known excitation, we propose using the anechoic handclap recordings to train a deep neural network with a supervised regression objective. Evaluated on a controlled synthetic benchmark, the proposed neural regressor significantly outperforms windowing-based baselines across all instrumental metrics. Furthermore, we test the proposed method on handclap recordings measured in real acoustic spaces, showing that the inferred RIR spectra are consistent across different handclap measurements taken in the same room location. These results showcase the feasibility of directly estimating RIRs from natural handclaps without requiring knowledge of the excitation signal.

We study a globally coupled stochastic system in which each unit carries an Ising spin and a continuous phase. The spins undergo Glauber switching with relaxation rate $\gamma$, while the phases are driven by Ornstein-Uhlenbeck noise with correlation time $\tau$. A spin-dependent phase interaction supports a composite coherent mode, $Z_m=N^{-1}\sum_j\sigma_j e^{i\theta_j}$, that can order even when the ordinary phase coherence is small. Linear response about the nonmagnetic incoherent state gives the synchronization threshold $K_{\mathrm c}=[(\mu+\beta_s\gamma)\chi_\gamma]^{-1}$, where $\chi_\gamma$ is a memory-weighted Laplace transform of the free phase correlation function. The competition between the increasing Glauber response and the decreasing memory susceptibility produces a finite switching rate at which $K_{\mathrm c}$ is minimized. We derive a general sufficient condition for such an interior optimum and show that finite-time Ornstein-Uhlenbeck correlations satisfy the required fast-switching asymptotics, whereas the white-noise limit need not. Finite-size simulations reproduce the nonmonotonic threshold, its shift toward slower switching as $\tau$ increases, antiphase composite order in a nonmagnetic state, and mode mixing on a magnetized background.

Quantum physics underpins the emerging quantum technology era, yet its counterintuitive principles remain challenging for beginners. Video games offer a promising medium to make these principles accessible through an interactive experience. Conventional gameplay, even when featuring extraordinary abilities of the protagonist, largely draws on classical intuition, shaping the player's reflexes through familiar expectations of motion, action, and consequence. Here, we propose extending these reflexes into the quantum domain by embedding superposition, unitary evolution, quantum gates, and measurement into the game. Central to this approach is a new controller action, the Gate of Fate, which allows players to engage in quantum operations through their gaming decisions. We demonstrate the concept in a Tetris-based prototype, with progressively structured levels that introduce quantum operations and their consequences. We also outline extensions to role playing games, in which the behavior and difficulty of antagonists can respond to player's developing quantum gaming reflexes. By turning abstract quantum concepts into actionable game mechanics, this approach aims to cultivate quantum intuition through play, offering opportunities for both quantum pedagogy and more sophisticated game design.

For an $r$-uniform hypergraph $H$, let $\nu(H)$ be the maximum number of edges no two of which share $r-1$ vertices, and $\tau(H)$ the minimum number of $(r-1)$-sets such that every edge contains one of them. Aharoni and Zerbib conjectured that $\tau(H)\le\lceil\frac{r+1}{2}\rceil\,\nu(H)$, which for $r=3$ generalizes Tuza's conjecture on triangles. We prove that the fractional relaxation $\tau^*(H)$ of $\tau(H)$ satisfies $\tau^*(H)\le\frac{r+1}{2}\,\nu(H)$. This constant is best possible for every $r$, and for $r\ge4$ it improves on the previous bound of roughly $3r/4$.

With the constant advancements in AI, one possibility is to model agents after humans and, in turn, use these agents to carry out synthetic interactions. Such models could be used to predict interactions between their real counterparts, or potentially interactions at larger scales. In this paper, we test a more controlled version of this question through chess. We use 8 elite chess players, seal their direct pairwise games, learn each player independently using different methods, and then compose the resulting models on the withheld dyads. To evaluate the generated interactions, we use two measurements: opening-family total variation distance and win-draw-loss (WDL) total variation distance. M1 primarily improves WDL fidelity while producing smaller opening-family improvements, whereas M2 produces much larger opening-family improvements while having little effect on WDL-TV. For opening-family behaviour under M2, the correct assignment of the eight learned player identities also gives the closest match among all $8! = 40{,}320$ possible assignments. These results show that at least some properties of previously unseen interactions can be recovered from independently learned individuals. The partial recovery observed here may reflect limitations of the current individual modelling methods rather than a fundamental limit on compositional interaction recovery. An additional post-hoc method that combines the two mechanisms improves both measurements, suggesting that recovery across these behavioural properties is not necessarily mutually exclusive.

Quantum SDKs such as Qiskit are revised continually, and a single transpiler-pass change can introduce a software regression, so continuous integration (CI) must select and prioritize tests from a large, cost-heterogeneous suite under a fixed budget. We present a leakage-safe, cost-aware regression-test-selection methodology for the Qiskit quantum transpiler, with a pre-registered, budget binding evaluation that avoids data leakage. The evaluation uses a cost-heterogeneous corpus (116 units, per-unit cost spread 9,945X, T_full = 69.17 s) whose budgets were fixed from measured cost before any test-oracle label was read. A transparent risk_score selector does not beat simple test case-prioritization baselines: mean detection-vs-budget AUC is 0.721 [95% CI 0.44, 0.94] versus 0.874 [0.65, 1.00] for diversity-only (Cliff's {\delta} = -0.64, large), with cost/history/change-stage baselines at 0.840 and random at 0.821. A component ablation shows the composite underperforms its own best signal: diversity and novelty, not severity or cost, are the effective signal. A second, independently pre-registered evaluation (19 mutation-testing events: nine original plus ten new, verified operators) tests the decomposed, diversity-first selector this mechanism implies: it closes the gap to the strongest baseline to a negligible effect size (0.880 vs 0.880, {\delta} = -0.08) while decisively beating the original composite (0.880 vs 0.768, {\delta} = +0.57). Two verified forward-regression events from real Qiskit CI history corroborate it, reported per event, not pooled, under a pre-declared claim-scope rule. We report the negative result as an honest, pre-registered finding with its mechanism. All code, data, and artifacts from this empirical software engineering study are released for reproducibility.

Running a language model on edge hardware provides private and low-latency reasoning without a network connection, and yet the small models that fit on such devices are unreliable on the tasks computers are expected to handle well, such as arithmetic, algebra, and formal logic problems. We argue that much of this unreliability is avoidable. Many queries appearing to demand reasoning are in fact structurally deterministic and permit fast and exact symbolic solutions. Therefore, forcing a probabilistic model to approximate them sacrifices accuracy and energy for little benefit. We present a neurosymbolic router that classifies each incoming query and dispatches it to the cheapest correct solver, sending structured tasks to deterministic engines and reserving the small language model (SLM) for open-ended word problems. Instead of hand-coding the routing logic, we learn a deterministic finite automaton (DFA) with the L* grammatical inference algorithm, using the SLM as a membership oracle and labeled data as an equivalence oracle. On a Raspberry Pi 4B (8 GB RAM, no GPU), evaluated on 100 untested prompts from DeepMind Mathematics, GSM8K, and RuleTaker, learned routing attains 100% routing accuracy and 98.3% overall accuracy with a 512-token reasoning budget (93.3% on word problems), compared with 72.0% for the strongest agent baseline, Program-of-Thought, and 58.7% for a tool-calling agent given the same solvers. Since formatted queries never reach the model, the router answers them in 1-11 ms and, in its 30-token configuration, runs 8.8x faster and 2.8x more energy-efficient than Program-of-Thought.

Optimal Transport (OT) provides a principled framework for comparing and transforming probability distributions while preserving geometric structure. Recently, OT has gained significant attention in machine learning due to its ability to measure discrepancies between distributions, even when their supports do not overlap, making it effective for tasks such as generative modeling, domain adaptation, and transfer learning. Despite its success in fields such as computer vision and natural language processing, OT remains relatively underexplored in speech research. Speech signals present unique challenges, including temporal dynamics, speaker variability, noise, reverberation, and heterogeneous multimodal representations involving audio, text, and visual information. These factors often lead to distribution mismatches, where OT offers a natural framework for alignment and interpretation. This work aims to promote broader adoption of OT in speech processing by: (1) reviewing OT foundations through intuitive physical interpretations and highlighting connections to modern generative models; (2) presenting computational algorithms suitable for deep learning frameworks; and (3) demonstrating OT applications in cross-domain and cross-modal speech tasks, including speech enhancement, automatic speech recognition, language and speaker recognition, and audio spoof detection. We highlight OT's strong potential for addressing distributional variations in real-world speech applications.

Maximum likelihood estimation of Markov deterioration hazard models for infrastructure asset management is sensitive to the numerical conditioning of explanatory covariates, yet production pipelines often adopt a single scaling convention without systematic justification. We study four covariate scaling transformations—baseline max scaling, min-max scaling, z-score scaling, and Box-Cox transformation with a training-derived positivity shift—applied to an Exponential Hazard Markov (EHM) model estimated via L-BFGS-B on bridge inspection transition data.

Audio-only pedestrian detection is attractive for urban sensing but limited by weak acoustic cues. An appealing strategy is cross-modal knowledge distillation, in which a video teacher supervises the audio student during training so that the deployed model runs on audio alone. Under this task's severe class imbalance and wide video-audio modality gap, however, what such distillation contributes is unclear. We introduce Trust-Filtered Distillation (TFD), which selectively suppresses teacher supervision on pedestrian samples, and interpret its logit formulation as conditional label smoothing under a shared temperature. Across ten distillation configurations under five-fold cross-session validation on ASPED, most methods yield modest gains in macro accuracy accompanied by small changes in PR-AUC. The main effect is higher no-pedestrian accuracy at the cost of lower pedestrian recall. Adding TFD to logit distillation strengthens this trade-off without improving mean PR-AUC. These findings clarify the benefits and limitations of selective cross-modal supervision by distinguishing operating-point shifts from discrimination gains in imbalanced acoustic detection.

Open-weight models are often released, fine-tuned, aligned, merged, and re-released, making provenance audits ask not only whether checkpoints are related, but also which checkpoint came first. Many existing model-provenance methods are designed for a base-known audit setting: given a victim or source model, they test whether a suspect model is related to it. Although these audits are framed as source-to-suspect tests, their underlying evidence is often symmetric, relying on representation similarity, weight similarity, behavioral fingerprints, or correlation statistics. Symmetric pairwise comparisons can detect relatedness, but they cannot by themselves orient relationship between checkpoints A and B. We therefore introduce a local geometric comparison: instead of comparing two checkpoints directly, we add a third same-family checkpoint as a witness and compare the geometry around each candidate endpoint. Direction is inferred by asking which candidate behaves more like a branching parent. Motivated by this idea, and by the empirically observed asymmetry between parent-anchored and child-anchored witness-overlap distributions, we propose Witness Overlap, a prompt-free, training-free white-box test for directional provenance. On 176 LLM checkpoints from 16 families, our one-witness test orients 95.3% of parent-child decisions using Frobenius cosine. We further evaluate root identification, sibling discrimination, generalizations to VLM and diffusion families, and chain-structured ordering. The signal is robust to weight noise and sparse pruning, with a proposed SVD weight reduction variant showing greater robustness than Frobenius cosine.

Given a point set $[n]$ and a collection $B$ of $k$-subsets of $[n]$, we create a monomial ideal whose Betti numbers completely determine whether the pair $([n],B)$ is a Steiner system $S(t,k,n)$. In particular, our construction characterizes Steiner triple systems and Steiner quadruple systems solely on the basis of Betti numbers of monomial ideals. Moreover, these monomial ideals allow us to reformulate the renowned prime power conjecture as follows: If a monomial ideal $M$ of $S = K[x_1, \dots, x_{q^2+q+1}]$ generated by squarefree monomials of degree $q+1$ has Betti numbers $\mathrm{b}_s(S/M) = {{q^2+q+1} \choose s} \text{ for all } s=0,\ldots,q$ then $q$ is a prime power.

Sudakov minoration asks whether a large family of separated random linear forms must have a large expected maximum. We present a proof candidate for this principle for all unconditional log-concave vectors. The argument starts with a classical reduction to sparse coordinate supports. It then selects one feasible threshold witness for each label, removes a common coordinate core, and controls the remaining overlaps. The main analytic step is an exponential-moment estimate for a softened witness payoff. We obtain it by combining a one-dimensional clipping inequality with triangular transport, using log-concavity of the source and sign symmetry of the target. A Bernoulli comparison restores the signs at the end. The exposition includes historical context, a guide to the proof, all intermediate arguments, and explicit choices of constants. Two consequences concern covering numbers in the moment metric and concentration of bounded functions of the magnitudes.

This paper considers the generic behaviour of sheaves supported on Schubert varieties in finite flag varieties. Our main results are that, for any fixed prime $p$, as the rank of the associated algebraic group grows, almost every intersection cohomology sheaf admits $p$-torsion in its stalks or costalks, and almost every indecomposable parity sheaf is not perverse. For certain families of partial flag varieties we also determine explicit asymptotics for this growth.

Modern text-to-image models produce high-fidelity images but still struggle with compositional prompts that require instance identity, attribute ownership, counting, spatial ordering, and role-sensitive relations. We introduce Panoptic Scene Program Diffusion Transformer (PSP-DiT), a diffusion-transformer architecture that treats a panoptic scene program as a first-class latent variable rather than an external control signal or post-hoc parse. PSP-DiT jointly denoises image latents and scene-program latents through coupled transformer streams, while panoptic grounding and cycle-consistency objectives tie object instances, attributes, relations, and counts to visual support in the generated image. Under matched training and inference settings, PSP-DiT improves over a strong flat-text baseline across GenEval 2, SANEval-Simple, PSG-Score, and DetailMaster, with the largest gains on counting, attribute binding, role-sensitive relations, and long structured prompts. The method preserves image quality, adds modest inference overhead, and remains robust to imperfect scene programs.

The polynomial Bohnenblust–Hille inequality controls the coefficient $\ell_{2m/(m+1)}$-norm of an $m$-homogeneous polynomial by its supremum norm, with a constant independent of the dimension. We study the associated Bohnenblust–Hille ratio from a probabilistic point of view, by placing normalized surface measure on the Euclidean coefficient sphere. Our results reveal a sharp contrast between the extremal behavior governing the classical Bohnenblust–Hille constants and the typical scale seen in coefficient directions. For arbitrary prescribed monomial supports, the ratio is eventually at most $1$ almost surely, and it tends to zero in spherical measure exactly when the number of monomials tends to infinity. On the full complex polynomial spaces we determine its typical asymptotic scale uniformly in the dimension; in the critical regime $n_m/m\to1$ this gives $2\sqrt2/\sqrt{m\log m}$, in contrast with the nonvanishing extremal scale. For real polynomials, the corresponding ratio tends to zero in spherical measure exactly when the number of variables tends to infinity.

A wavefront-sensor (WFS) prediction can select the photon measurement before detection or condition its likelihood afterward. This matters for reflected-light spectra requiring hundreds of hours, because subtracting residual starlight cannot remove its photon noise. In a two-mode, low-occupation model, isotropically distributed leakage makes planet-mode projection—ideal single-mode injection matched to the planet—the optimal fixed single-photon measurement, including unequal aligned backgrounds and equal Poisson detector-event rates per output. For nonzero leakage, an attainable two-output conditioned measurement is optimal and strictly more informative before differential loss. For an isotropic background, a contrast bound holds for any distribution of recorded leakage directions: relative transmission $0.80$ and relative admitted-time duty $0.90$ limit the Fisher information per scheduled time to $0.81$ of the fixed optimum at equal predictable-leakage and planet contrasts. Haar averaging sharpens this ceiling to $0.78$. The necessary leakage-to-planet ratios for gain are approximately $2.25$ for any direction law and $3.26$ for Haar directions. A concentration-model certificate identifies directional diversity sufficient to beat recalibrated fixed measurements. Independently gated fixed-basis fallback guarantees no loss of continuum-profiled spectral information when rates and costs are known. For the Habitable Worlds Observatory, the candidate regime is predictable, directionally diverse, leakage-dominated residuals, not a general sensitivity improvement.

Magnetic resonance imaging involves an inherent trade-off among spatial resolution, acquisition time, and noise. This trade-off contributes to long scan times and high cost. Deep learning has improved image denoising, but cardiac MRI remains difficult because high-resolution, rapid acquisitions generally lack corresponding low-noise ground truth. Self-supervised denoising offers a potential solution by learning from noisy image pairs or even single noisy acquisitions. However, we show that Noise2Void-style blind-spot denoising, which uses a mean squared error (MSE) loss and assumes zero-mean, independent and identically distributed (i.i.d.) noise, is poorly suited to MR magnitude images. When applied to short-axis $T2$-weighted and $T1\rho$-weighted cardiac MRI with synthetic Rician noise, it produces biased denoised images and biased parametric maps of $T2$ and $T1\rho$. To address this limitation, we formulate self-supervised denoising as maximum likelihood estimation under a known Rician noise model. This yields unbiased denoisers that are competitive with supervised baselines.

In this study, the power law form of f(Q) gravity $(f(Q)=Q+mQ^n)$ has been studied in view of statistical analysis with current observed data and irreversible thermodynamics. The best fit values of model specific parameters are found with the use of of 31point Hubble data, Patntheon type Supernva and 1721 point SH0ES data and a comparative study has been performed between $f(Q)$ and standard $\Lambda$CDM model. The thermodynamic consequence using standard Eckart theory of non-equilibrium thermodynamics has been examined independently for general form of $f(Q)$ gravity followed by power law form of $f(Q)$ where the horizon entropy is calculated using unified law of thermodynamics. Suitable range of power law model specific parameters has been explored through investigating validity of generalized second law of thermodynamics and thermodynamic equilibrium. Finally evolution nature of cosmographic parameters are studied within the specific range of $m,n$ which is compatible with the results obtained from both statistical and thermodynamical analysis.

Artificial intelligence (AI)-based weather prediction is approaching the skill of physical numerical weather prediction (NWP) systems at a fraction of the computational cost. This is particularly promising for Africa, where rainfall extremes are intensifying and many forecasting centres lack the infrastructure to run physical models at extended lead times. We present a calibrated comparison of GraphCast, GenCast and the Functional Generative Network (FGN) against the physical NWP model IFS for rainfall prediction across Africa. Deterministic and probabilistic forecasts are postprocessed using Isotonic Distributional Regression and evaluated with the Continuous Ranked Probability Score against IMERG, RFEv2 and CHIRPS across seasons, wet and dry regimes, elevation zones and lead times. All models retain skill beyond climatology across most seasons and at extended lead times. AI models generally outperform IFS in wet regions, whereas IFS performs better in dry, high-elevation areas, where its finer resolution better represents orographic controls on rainfall. Across observational datasets and seasons, AI models achieve a median improvement of approximately 5% over IFS. GraphCast achieves calibrated skill comparable to the ensemble-based FGN, although FGN provides greater significant skill at longer lead times. These results highlight the potential of calibrated AI weather prediction to provide accessible and computationally efficient rainfall forecasts across Africa, while demonstrating the continuing importance of spatial resolution, ensemble design and regional characteristics.