Papers

The incorporation of AI into the assessment of physics laboratory reports offers opportunities to support the review of student work and the provision of feedback. This article revisits an experience involving the use of ChatGPT models to analyze laboratory reports and examines the conditions that influence their usefulness in teaching practice. The analysis considers the evolution of AI models, document-processing procedures, and different modes of interaction, with particular attention to the effective availability of evidence contained in student reports. The findings indicate that differences between AI-generated and teacher assessments may be related not only to model capabilities but also to difficulties in retrieving and interpreting equations, graphs, tables, units, and other visual elements. The possibilities of systematic processing of sets of reports and conversational review of cases requiring more focused analysis are also examined. Based on these observations, a working strategy is proposed in which AI serves as a complementary resource for organizing assessment, supporting feedback, and identifying recurring difficulties in student work. The analysis highlights the importance of document-processing conditions and evidence availability, as well as the teacher's role in interpreting AI-generated information and making evaluative and pedagogical decisions.

We show that if a sequence of expander graphs equi-coarsely embeds into a Banach space, then this Banach space fails Kasparov and Yu's Property (H). Consequently, no Banach space with Property (H) can be coarsely universal for all countable groups. We provide a Lean verification of our results.

Complex-valued Transformers have inherited softmax attention over the raw complex inner product. Outside natively complex domains this standard form stays near chance, and no complex attention had been shown to correct it. We show that the match must be a scaled cosine score: L2-normalise queries and keys, so the score reads their cosine similarity and ignores their magnitudes, and hold that score at order-one scale. With this the same models train on four diagnostic tasks under two different gates; without the normalisation they stay at chance on ListOps and Needle under both gates and fall far below on the other two, and a normalised score placed at too small a scale fails as well. The resulting family of phase-coherent Transformers (\PCT) matches or exceeds the strongest real-valued baseline across long-range memory, positional retrieval, hierarchical reasoning, frequency-domain classification and physical complex signals; it shows no degradation up to depth 20; and its loss decreases log-linearly over a 61-fold range of parameters. A member of the family, complex screening combined with a phase-coherent recurrence, is the first genuinely complex-valued neural network to solve Path-X, with 91.6% of its trainable parameters complex-valued against 38.2% for S4. We record these as signs of generalisation not previously seen in complex-valued neural networks.

We study the canonical formal solution space of a homogeneous $A$-hypergeometric system in a generic direction. We present as a finite-dimensional cokernel the quotient of that space by the span of the series obtained by intrinsic perturbation, taken over all exponents occurring in that space and all ordered negative support families, and we compute the codimension of that span. We show that the presentation and the codimension transfer to the holomorphic solutions on a common nonsingular domain. We apply these results, for every integer $q\geq 1$, to a homogeneous $A$-hypergeometric system of lattice rank 2 with $5q$ columns. We show that the canonical formal solution space of this system has dimension $12q^2$ and that the span of the series obtained by intrinsic perturbation has codimension exactly $\lceil 3q^2/4\rceil$ in that space.

Let $\Omega\subset\mathbb R^2$ be a smooth bounded domain containing the origin and invariant under reflection across the coordinate axes, and let $0<\lambda<\lambda_1(\Omega)$, where $\Lambda_1 (\Omega)$ is the first eigenvalue for $-\Delta$ on $\Omega$ under Dirichlet boundary conditions. For every fixed integer $k\ge1$ and all sufficiently small $\varepsilon>0$, we construct a positive solution of \[ -\Delta u=\lambda u e^{u^{2+\varepsilon}} \quad\hbox{in }\Omega, \qquad u=0\quad\hbox{on }\partial\Omega, \] which blows up at the origin as a tower of $k$ Liouville bubbles. The concentration scales are strongly separated. The proof is based on a Lyapunov–Schmidt reduction adapted to these different scales.

Estimating the dynamic aperture of circular particle accelerators typically requires expensive long-term tracking. Using classical homology, we construct a two-dimensional theoretical classification of regular and chaotic orbits and use persistent homology for its numerical implementation on short orbit segments. In four dimensions, we introduce topological chaos indicators based on persistent homology and use normal-form theory to apply the classification to two symplectic-plane projections. The methods reproduce the expected organization of regular and chaotic motion in several canonical Hamiltonian systems. Applied to symplectified one-turn maps of a nonlinear lattice model of the Integrable Optics Test Accelerator, the results obtained from the first 200 turns identify the central connected stability region and its surrounding transition to chaos. They are consistent with the short-term dynamic aperture of the electron configuration obtained from $10^4$ turns and the long-term dynamic aperture of the proton configuration obtained from $10^8$ turns. For the configurations studied, persistent homology of short orbit segments predicts the dynamic aperture obtained by substantially longer tracking, potentially reducing the need for exhaustive simulations in studies of existing accelerators and the design of future facilities. The methods could also complement classical chaos indicators and modern approaches based on artificial intelligence.

Scanning Electron Microscopy (SEM) is a foundational technique for characterizing material microstructure, which dictates many fundamental physical and chemical properties. With the rise of Self-Driving Labs (SDLs), samples are now synthesized in large batches, demanding equally high-throughput, autonomous characterization. Existing automated electron microscopy pipelines are task-specific: they detect pre-defined features, optimize known properties, or require prior knowledge of the sample, restricting each pipeline to the material system it was built for. We introduce AutoRASOR, a task-agnostic autonomous SEM pipeline that captures the multi-scale morphology of an unknown sample without domain-specific pre-training, fine-tuning, or human prompting. AutoRASOR embeds micrographs in real time with a vision foundation model (VFM), DINOv3, and selects regions of interest (ROIs) through two complementary policies: Latent Farthest Point Sampling (LFPS) and active learning on morphological ambiguity, which is the conditional variance of unresolved fine-scale features given lower magnification appearance. Active learning on ambiguity consistently captures more diverse and rare morphologies than random ROI selection, while LFPS reliably recovers the specimen's morphological distribution within a limited capture budget, tested both on real SEM micrographs and synthetic phase-field images. By shifting autonomous characterization from pre-defined, task-specific targeting of features to morphological survey, AutoRASOR generates information-rich multi-scale datasets for diverse downstream tasks. Without the need for domain-specific pre-training or prior material assumptions, this framework can be deployed out-of-the-box to characterize novel materials produced by SDLs.

Inferring 3D cellular properties from 2D microscopy is difficult when a reference instrument reports only population statistics rather than labels for individual cells. Here we develop a population-supervised framework that maps single 2D red-cell images to latent biophysical quantities and aggregates them to mean corpuscular volume, red-cell distribution width and mean corpuscular haemoglobin. The model combines shared local inference, a biophysically structured decoder for volume and haemoglobin, learned instance weighting and device-specific calibration. We formalise conditions under which aggregate observations identify restricted instance predictors, show why population agreement does not by itself identify single-cell properties or 3D geometry, and derive the dispersion penalty induced by subset mean matching. The development dataset comprises 390 specimens and 1,105 acquisitions across six devices, with reported Pearson correlations of 0.86–0.98 against a Sysmex analyser. The framework provides a testable route from 2D images and population supervision to 3D cellular biophysics without claiming explicit 3D reconstruction.

Understanding contextual causality is critical for large language models (LLMs), as it enables them to accurately identify causal relations in specific situations and support more reliable decision-making. Despite its significance, a systematic exploration of contextual causality with LLMs is still lacking. To fill this gap, we present a comprehensive survey on this topic. In this survey, we first propose a taxonomy of contextual causality, consisting of semantic, intervention, and counterfactual causality, and characterize each category by its core causal question, required model capabilities, representative tasks, and practical uses in causality analysis. We then analyze existing studies and discuss their key limitations. Finally, we examine the gaps between current benchmarks and real-world needs and outline promising directions for future research. Our goal is to clarify the research landscape of contextual causality with LLMs, emphasize its importance, and highlight promising future directions.

AI systems are becoming participants in the evaluation and use of scientific research. They encounter citation counts, download statistics and lists of popular articles developed around human readers, but the collective consequences of these signals for artificial readers remain uncertain. This paper adapts the Music Lab design to a market for academic attention. In the first experiment, 1,000 AI agents choose papers from the titles and abstracts of all 114 regular research articles published in the American Economic Review in 2025. The experiment has five independent-choice communities and five social-influence communities, each with 100 sequential agents. Only agents in the social-influence condition observe earlier selections within their community. Agents may select any number of papers. Social-information communities select 17.2 percent fewer papers per agent, concentrate their choices more heavily, and collectively cover 73 papers, compared with 90 independently. Between-community variation is greater under social information. In a second experiment with 200 agents across twenty social communities, randomly assigning papers five initial selections raises their subsequent selection rate by 45.55 percentage points (95% CI: 41.20 to 49.90). Choices have modest correspondence with external citations and little correspondence with download counts. The results show how a simple information rule shapes the volume, breadth and distribution of scientific attention in an artificial population.

Weighted Hardy inequalities on a domain $\Omega\subset\R^n$ can be deduced from lower Hausdorff-content bounds on suitable visible parts of the boundary, and it is natural to look for visible sets described by straight segments, which are easier to verify than the curve-based visual boundary of Koskela and Lehrbäck. We show that this approach is subject to an intrinsic obstruction. If a boundary point $\xi$ is seen from $x\in\Omega$ along a segment satisfying a uniform thickness condition, then $\Omega$ contains a truncated cone with vertex $\xi$; consequently the quantitatively straight visible boundary $\partial^{\mathrm{str}}_{x,\alpha}\Omega\cap B(x,C_0d_\Omega(x))$ is a finite union of Lipschitz graphs, is $(n-1)$-rectifiable, and carries no $\lambda$-Hausdorff content for any $\lambda>n-1$. Since content conditions with $\lambda\le n-1$ already imply the $(p,\beta)$-Hardy inequality for $\beta<p-n+\lambda$ without any visibility assumption, segment-based criteria are either unsatisfiable or redundant: they never reach the regime $\beta\ge p-1$ in which visibility is genuinely needed. We show that the exponent $n-1$ is attained, so that the rectifiability theorem is sharp; we exhibit a boundary point lying in the visual boundary of Koskela and Lehrbäck but in no $\partial^{\mathrm{str}}_{x,\alpha}\Omega$; and we observe that raw straight visibility, without the thickness condition, escapes the obstruction, is sufficient for $\lambda\le n-1$, and remains open for $\lambda>n-1$.

Let $\Lambda=KQ/I$ be a finite-dimensional zero-relation algebra. We encode Crawley–Boevey tree modules over $\Lambda$ by finite rooted trees labelled by arrows of $Q$ and their formal inverses, and construct a deterministic finite bottom-up tree automaton recognizing exactly these encodings. We define an accepted tree to be an automata-induced tree brick when it has no non-trivial factor–image self-overlap, and use Crawley–Boevey's graph-map basis to prove that this is equivalent to brickness of the associated tree module. We also introduce local colourings of $Q_1$ and show that the arrow alphabet can be compressed without changing the tree data, graph maps, or brick property. The optimal number of colours for such a compression is the maximum of the in-degree and out-degree of $Q$. We conclude by asking whether the tree language consisting only of bricks is regular.

Coherent hard exclusive reactions on light nuclei offer access to their quark and gluon structure and provide a framework for three-dimensional nuclear tomography. We analyze deeply virtual Compton scattering on a helium-4 target, including leading-twist contributions as well as kinematical twist-3 and twist-4 effects. We present numerical estimates of cross sections and asymmetries for kinematic regimes relevant to JLab experiments. We emphasize the importance of next to leading order (NLO) and kinematical twist 3 and 4 contributions to interpret data in the JLab kinematics. We deduce a first tomographic image of quarks and gluons in the helium-4 nucleus.

Over the last decade, behavior trees (BT) have become one of the dominant behavior models for coordinating missions of robotic systems. Yet empirical evidence on BT adoption in real-world contexts remains limited, especially regarding practitioners experiences and practices. Without practitioner-grounded evidence from both academic and industrial settings, the research community risks developing guidelines and tools that are plausible in principle but only partly aligned with real challenges. This scarcity of evidence leads to ad-hoc practices, impeding software reuse, maintenance, and evolution. This paper reports a mixed-methods study combining a technical action research investigation at an automotive company with a survey of 34 robotics practitioners. Our results indicate that BTs improve team communication and the understandability of robotic decision-making logic, reflecting BTs practical value beyond mission coordination. At the same time, practitioners face multiple non-trivial design and integration decisions, complicated by the lack of adequate guidelines and tool support. These decisions span architectural and language choices when implementing BTs and integrating them within ROS, for which we report observed patterns. Additionally, practitioners faced multi-factor granularity decisions and mixed experiences with current libraries. For the most used BT libraries, they reported implementation challenges and documentation gaps. Regarding planning algorithms, practitioners find deciding optimal BT node ordering challenging. Views on scalability remained inconclusive, and limitations in current libraries and practices hinder broader adoption. We conclude with cross-cutting observations and implications for both practitioners adopting BTs in robotic systems and researchers aiming to advance empirical understanding of BT adoption.

This paper describes experiments and numerical simulations on the normal impact of a round liquid jet onto a horizontal surface, such as when water from a tap hits the bottom of a kitchen sink. In this case the liquid impacting on the surface spreads as a fast-flowing thin film and, at some distance from the point of impact, the thickness of the flow abruptly increases and the speed of the flow is reduced. In the experiments studied here the flow is axisymmetric about the axis of the jet, and the abrupt change in depth occurs at a given radius and is known as a circular hydraulic jump (CHJ). We present new experiments in which we measure the thickness of the liquid film inside and beyond the jump and use these measurements to estimate the governing parameters, the Weber, Froude and Reynolds numbers that determine the influence of surface tension, gravity and viscosity, respectively. We also carry out numerical simulations of the flow that show excellent agreement with the experiments and provide independent estimates of these dimensionless parameters. We find that, on the scale of a kitchen sink, and for water at high Reynolds number and low Bond number, at the jump the Weber number is of order unity while the Froude number is large, implying that the jump is controlled by surface tension. We also define a critical dimensionless jet flow rate at which this control no longer holds and gravity plays a significant role.

Choose uniformly among the combinatorial types of convex three-dimensional polyhedra with a fixed admissible number $e$ of edges, and let $V_e$ be the number of vertices. This resolves a fixed-edge limit-distribution question posed by Rüdinger: if $\beta_e=V_e/(e+2)$, then $\sqrt e(\beta_e-1/2)\Rightarrow N(0,1/32)$, equivalently $\operatorname{Var}(V_e)\sim e/32$. Using the classical rooted enumeration and asymmetry results of Bender and Wormald, we derive a relative lattice local limit theorem on every $o(e^{3/4})$ window, a quartic correction from the rate function on every $o(e^{5/6})$ window, precise moderate-tail constants, a quadratic moderate-deviation principle for every $a_e\to\infty$ with $a_e=o(\sqrt e)$, and a full speed-$e$ large-deviation principle with an explicit good rate function. All fixed standardised moments converge. When $e=3m$, the two extremal vertex counts have equal probability asymptotic to $\frac{6561}{32\sqrt2}(4/27)^m$. Rooted and unrooted fixed-edge laws are also uniformly exponentially close, with relative discrepancy $O(\rho^e)$.

Sharing irregular longitudinal health records can accelerate model development, yet synthetic releases may leak participation, distort temporal dependence, suppress rare events, or reduce utility for underrepresented groups. We present TRUST LONGSYNTH, an auditable patient level private generator that combines bounded sufficient statistics, zCDP accounted Gaussian releases, conditional analytic score diffusion, block banded temporal covariance, separate missingness and gap models, and a protected event sampling floor with population weights. The method was evaluated on five independently generated, three cohort benchmarks containing 720 patients, fourteen irregular observation slots, six mixed variables, informative missingness, and a rare deterioration outcome. At epsilon = 12 and delta = 10 to the power of minus 5, TRUST LONGSYNTH achieved mean train synthetic test real AUPRC 0.342, Brier score 0.088, expected calibration error 0.082, correlation error 0.222, autocorrelation error 0.317, and membership attack AUROC 0.499. Relative to the private diagonal score baseline, AUPRC increased by 7.5 percent, while Brier, calibration, correlation, and autocorrelation errors decreased by 6.1 percent, 17.0 percent, 28.0 percent, and 30.1 percent, respectively. The method did not dominate every nonprivate or discrete baseline, and corrected paired tests were inconclusive with five seeds. Canary exposure was 1.8 percent, compared with 28.8 percent for DP Score in the same stress test. These findings support a transparent privacy utility fairness evaluation protocol, not clinical validity or unconditional release safety, and motivate governed external validation on real multi site records.

We investigate the Raman response of sodium-doped cuprate oxychloride Na$\_x$Ca$\_{2-x}$CuO$\_2$Cl$\_2$ high-temperature superconductors across their entire phase diagram, from the antiferromagnetic to the superconducting region. In addition to the expected Raman-active phonon modes, we detect several additional modes that can be interpreted as being excited via a resonance process enabled by strong electron–phonon coupling. To verify the resonance effect, the Raman response at different incident photon energies was measured. At high energies, there is a well-defined $B\_{1g}$ mode in the antiferromagnetic phase, which can be interpreted as a bimagnon We follow its temperature and doping dependence, providing information on the multimagnon excitation in these cuprates, which can be theoretically linked to the exchange interaction.

We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of $\mathbb{R}^d$. In dimension $d\leq 2$, we prove mass conservation (that is absence of gelation) when the coagulation coefficient satisfies the critical additive bound $a_{i, j} \leq C(i + j)$ for some constant $C > 0$. We thereby close the remaining gap between the spatially homogeneous setting and the spatially inhomogeneous diffusive setting. In dimension $d\leq 4$, we impose a higher decay rate on the coagulation and fragmentation coefficients, but we nonetheless prove regularity and absence of gelation under mild assumptions on the diffusion rates.

Accurate delineation of bi-atrial structures from late gadolinium enhancement MRI (LGE-MRI) is an important prerequisite for structural analysis and future fibrosis-quantification workflows in atrial fibrillation (AF). However, automated segmentation is challenging due to thin-walled anatomy, domain shifts across imaging centres, and limited benchmarking of existing methods. This study presents a two-stage segmentation framework and benchmarking platform for evaluating how ROI localisation, encoder design, 2D/3D dimensionality, and ensemble fusion affect bi-atrial wall and cavity segmentation across multicentre LGE-MRI datasets. The framework integrates 3D localisation and fine segmentation using 2D and 3D U-Net variants with ResNeXt encoders and compares them with convolutional, transformer-based, and state-space architectures. { Evaluation across three independent cohorts assessed accuracy and cross-domain transfer without target-domain fine-tuning. Cavity segmentation transferred more consistently across centres than atrial wall segmentation, while wall performance remained sensitive to domain shift, particularly in the Kobe cohort.} By quantifying how 2D, 3D, and ensemble architectures behave across centres and between walls and cavities, this work provides a reproducible benchmark for future methodological development and clinical validation.

Purpose: Contrast-enhanced breast MRI depends on intravenous gadolinium-based contrast agents, motivating methods that synthesise post-contrast appearance from pre-contrast images alone. The MAMA-SYNTH Challenge (MICCAI 2026 Deep-Breath Workshop) evaluates such synthesis across four metric groups: image fidelity, tumour region of interest, downstream classification, and downstream segmentation. The four group ranks are averaged, so optimising a single objective is insufficient. Materials and Methods: We developed a lesion-gated hybrid synthesis pipeline. A lesion probability map, estimated from the pre-contrast slice alone by an ensemble of pre-contrast-only segmentation networks, spatially coordinates a tumour-focused regression pathway and a background-focused Pix2PixHD synthesis pathway, followed by a region-dependent calibration of the predicted enhancement. Training used the public MAMA-MIA collection with a patient-level split. Inference consumes a single pre-contrast 2D slice, with no mask, no post-contrast image, and no auxiliary metadata beyond image geometry. Results: On internal validation (n = 120 patients) the method reached MSE 0.523, LPIPS 0.185, and tumour-region SSIM 0.495. It was submitted to the hidden external 300-case test cohort as a self-contained inference container. The method ranked sixth in the official MAMA-SYNTH Challenge leaderboard. Conclusion: A test-compatible lesion probability map derived from the pre-contrast image can coordinate complementary tumour-focused regression and background-focused perceptual synthesis, enabling balanced virtual contrast enhancement under a multi-metric challenge setting.

We study linear gravitational modes, sourced far-zone fields, and quadratic energy balance in a four-parameter tetrad theory of gravity. The theory contains three parity-even torsion invariants and a parity-odd coupling $v^\mu a_\mu$, where $v_\mu$ and $a_\mu$ are the vector and axial torsion components. Linearizing around Minkowski spacetime and applying a scalar–vector–tensor decomposition, we find two tensor, two scalar, and four vector degrees of freedom in the generic nondegenerate parity-violating region. The tensor and scalar modes propagate at the speed of light, while the two vector branches have coupling-dependent propagation speeds. We derive their kinetic eigenvalues, characteristic speeds, and flux normalizations. An exact trace identity shows that the vector Hamiltonian is not positive definite in the generic branch, even when the kinetic eigenvalues are positive and the propagation speeds are real. We also derive the response to a general compact canonical source and obtain explicit source-to-amplitude relations for all eight linear polarizations. The field $V_\mu=\partial^\nu B_{\nu\mu}$ is used to illustrate intrinsic-spin multipoles. {We further prove that the quadratic Noether current equals the second-order Møller current for the chosen first-derivative tetrad Lagrangian and derive the corresponding mode-resolved energy and momentum fluxes.} The vector contribution remains a formal signed response because of the unbounded Hamiltonian. The stationary limit reproduces the results of Ref.~\cite{ShirafujiNashed1997}, and a representative parameter scan illustrates vector-mode splitting and kinetic degeneracy.

Passive Helmholtz-resonator earplugs aim to attenuate hazardous noise while keeping speech audible; the air volume of an ear-sized shell is finite, and we treat it as the resource a design spends. For a vented bore transparent at zero frequency and loaded by reactive side branches, causality fixes a conserved integral of transmission loss. We derive it in device variables, add viscous and flanking constraints, and allocate the budget by hazard-weighted water-filling with a continuous speech-cost price. The audio-band budget B_ad = (20/ln10) pi^2 V / 2cS is set by the ratio of total cavity volume V to bore area S; occluding plugs are exempt. The f^2 price signal favours frequencies well above the source peak. Replacing strict transparency by a speech-cost price gives an exchange rate of about 1.3 dB of protection per decibel of speech cost under the present model, with the budget setting where it saturates. Across three form factors, low-frequency-selective designs stay near a decibel while hazard-matched mid/high-frequency designs reach twelve. The binding variables are bore area and speech allowance, not resonator count.

An APN mapping $F:\mathbb{F}_{2^n}\to \mathbb{F}_{2^n}$ is a polynomial characterized by the non-vanishing property on 2-flats. In this work, we analyze notions that are closely related to this property. To understand which $k$-flats of $\mathbb{F}_{2^n}$ remain flats under $F$, we study the $k$-breaking. The function $x^{-1}$ has been studied in the past in this context—we extend this study to general mappings and characterize the 2-breaking of APN functions. Recently, two generalizations of the APN property have been introduced: $k$-strongly non-normality and $k$-th-order sum-freedom. Sum-freedom generalizes the non-vanishing property of APN functions to higher dimensional flats. We provide in-depth observations of the relations between the breaking property, strongly non-normality and sum-freedom. We introduce a fourth concept called $k$-strongly breaking, which implies the breaking property. We derive several structural results for both notions and give a characterization of a subclass of APN functions in terms of the 2-strongly breaking property. We propose a different perspective of the non-vanishing property via a natural character transformation, which is closely related to the sum-of-square indicator of the components of $F$. We derive a precise value for the total sum of the sum-of-square indicators of $F$. With this approach, we provide a simple answer to Open Problem 4 in IEEE Trans. Inf. Theory 52(9): 4160-4170, 2006. Moreover, it allows us to explore balancedness properties of polynomials, one of which characterizes component-wise APNness, for odd $n$, and provides a natural extension to any dimension. We show that Dillon's APN permutation and the Gold functions satisfy a related property, termed $k$-balanced, which is presented under our framework.

Let $r,t\ge 3$ be integers and $L=\{\ell_1,\ell_2,\ldots,\ell_s\}\subseteq [0,r-1]$ a fixed set of integers with $|L|\neq r$ and $\ell_1<\ell_2<\cdots<\ell_s$. For each integer $n$, let $\Psi_{r}(n,L,t)$ be the maximum number of $r$-cliques in an $n$-vertex graph whose $r$-cliques, viewed as a family of $r$-subsets of the vertex set, form a $t$-wise $L$-intersecting family. In this paper, we prove that $\Psi_{r}(n,L,t)=o(n^{|L|})$ when the sequence $\ell_1,\ell_2,\ldots,\ell_s,r$ does not form an arithmetic progression, and we give an asymptotic formula for $\Psi_{r}(n,L,t)$ when this sequence does form an arithmetic progression. When $t=2$, our results are exactly Helliar and Liu's results.

Image steganography hides secret message within normal images, with most existing works relying on cover-preserving transmission. However, such a paradigm becomes vulnerable once the original cover is exposed or can be reliably approximated. In this paper, we propose StyleStegaNet, a stylized image hiding framework that replaces cover matching with style-concealment transmission. Instead of transmitting a cover-like stego image, StyleStegaNet generates stylized stego images conditioned on publicly available style references, redefining steganography invisibility from cover-preserving concealment to behavior-level camouflage based on style transformation. Such a setting poses a substantial challenge to reliable secret recovery, since neural stylization can significantly alter the feature statistics exploited by deep hiding methods. To address this challenge, StyleStegaNet decouples the overall task into four coordinated stages: stego generation, stylized transmission, structure-preserving reconstruction, and secret recovery. Moreover, StyleStegaNet is optimized with a progressive three-stage training strategy, in which wavelet-domain constraints and perceptual supervision guide the recoverable information toward structural representations. We further provide an analysis showing that secret recoverability is largely restricted to the normalized structural subspace, offering a mechanistic explanation for why directly stylized baselines fail and why a reconstruction-guided recovery path is necessary. Extensive experiments on DIV2K and MS-COCO datasets demonstrate the effectiveness of StyleStegaNet. And few-shot image steganalysis with two deep detectors further shows detection accuracy near random guessing, approximately 51%.

We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed. Two ports reveal the sum modulo two of the transmitted symbols with retention probabilities $\pg>\pb$; their roles are interchanged by an unknown state that remains fixed during the block. With one observation per channel use, no transmitter feedback, and zero switching cost, the region is $R_1+R_2\le\pg$ for every fixed error threshold below one, and a strong converse holds. For error thresholds below one half, the largest open-loop sum rate is $(\pg+\pb)/2$, whereas a fixed port permits only $\pb$. A causal receiver attains the larger region by learning the state from erasure flags while using every channel use for data. A posterior port rule makes only finitely many incorrect selections almost surely, with a uniformly bounded expected number of mistakes. Exact random linear-code formulas and output-counting converses quantify the finite-block consequences. At blocklength 256 with $(\pg,\pb)=(0.9,0.4)$, independent numerical validation supports 214 message bits at a one-percent ensemble failure target, compared with 148 bits for the best open-loop allocation in the same code ensemble. The resulting 44.59% increase is achieved with the same transmission and observation budgets. The analysis exhibits an explicit capacity gain from controlling the observation axis and separates that gain from information lost after a record has already been formed.

Background: Four-fold accelerated sensitivity encoding (SENSE4) can shorten brain MRI acquisition time but may amplify noise and result in residual aliasing artifacts after conventional reconstruction. Purpose: To evaluate whether an image-domain refinement framework can improve the quality of SENSE4 brain MRI while preserving anatomical information for quantitative measurements. Methods: In this prospective paired study, 80 participants underwent fully sampled and four-fold accelerated SENSE T1-weighted MRI. We developed an Anatomy-aware Residual Attention Network (ART-Net) to refine accelerated reconstructions through generalized self-attention and correlation-based residual artifact regularization. Participant-level splitting yielded training, validation, and independent test cohort (45/5/30 participants). The independent test cohort underwent quantitative, segmentation-based, and blinded radiologist assessments of image quality and anatomical preservation. Results: ART-Net demonstrated highly competitive reconstruction performance, achieving the highest peak signal-to-noise ratio (31.03 +/- 2.88 dB) and structural similarity index (0.963 +/- 0.022) among evaluated methods. It also demonstrated improved anatomical fidelity, with numerically highest Dice coefficients for medial temporal structures relevant to atrophy assessment (0.8824 +/- 0.0827) and whole-brain regions (0.8857 +/- 0.0885). Moreover, ART-Net improved gradient fidelity, regional contrast preservation, and radiologist-rated structural quality. Conclusion: ART-Net improved agreement between SENSE4 and fully sampled T1-weighted images in a single-center, held-out test cohort while maintaining segmentation-derived anatomical measurements. These findings suggest that ART-Net may support accelerated brain MRI by improving image fidelity and enabling reliable downstream anatomical analysis.

We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit. The physical–observation dual-axis formulation makes the observation kernel a design variable subject to explicit causal and resource constraints. For two equiprobable, initially unknown block states, matching converses and coding constructions give exact sum capacities of 1, $4/3$, and 2 bits per channel use for fixed-port, open-loop, and causal policies, respectively. These results hold for every fixed joint error threshold below $1/2$, under both average and maximal message error, with error averaged over the block state. Every receiver makes one observation per slot and switches ports at most once; the transmitters receive no feedback and the receivers do not cooperate. Causal observation thus doubles the optimal fixed-port sum capacity and exceeds the optimal open-loop sum capacity by 50%. With independent erasures of retention probability $p$, the exact causal region is $[0,p]^2$. A finite-blocklength bound accounts jointly for state-identification pilots and coding redundancy. We also optimize observation policies for fixed codes: an exact finite-horizon solution reduces message error from 10.76% to 7.52%, and a second-order approximation bound controls optimization over continuous observation directions. Linear-array designs and coding experiments examine the corresponding training, reliability, and control costs. The capacity result identifies a setting in which observation design removes the entire interference penalty, with the gain established by a converse as well as an achievable construction.

In this article, on Descartes' famous "circle theorem," we first attempt to explain how the philosopher could have arrived at the equation that he presents without demonstration in a letter to Princess Palatine Elizabeth of Bohemia in November 1643 (a previously unpublished proof, to our knowledge). Then we report some stages of the subsequent generalization of this theorem, whose Cliffordian flavor, via the equivalence of a quadratic form and the square of a linear form, still mobilizes mathematicians today. This statement, which, over time, has undergone different extensions, Euclidean and non-Euclidean, has found, in fine, a spinor formalization. We see there the proof of what we may call, in a Bachelardian style, an "inductive value" of the truth, which extends by successive generalizations. We conclude, more briefly, with the contacts between Elizabeth and Descartes, and the perhaps symbolic meaning of these considerations on "kissing circles," as they are called in Anglo-Saxon countries, in the context of their correspondence on the soul and the body, and the question of passions.