Papers

We present a spectral and timing analysis of X-ray emission from the actively accreting supermassive black hole (SMBH) in RX~J1301.9+2747 with prominent quasi-periodic eruptions (QPEs) using ASCA, ROSAT, XMM-Newton, and NICER observations. NICER detected renewed QPE activity from this source in 2024. We examined in detail the X-ray spectrum formation in this source during QPE outbursts applying the first-principal model, Bulk Motion Comptonization. We find an increase of the photon index $\Gamma$ with a mass accretion rate $\dot M$, the index saturation at $\Gamma_{sat}=2.7\pm 0.1$ at high $\dot M$ value during outburst peaks. Based on the derived $\Gamma-\dot M$ correlation, we apply the scaling technique for the first time to measure the black hole mass in RX~J1301.9+2747. The SMBH mass in this source was estimated to be between $4\times 10^5$ M$_ {\odot}$ and $7\times 10^6$ M$_ {\odot}$ for the inclination range from 0$^{\circ}$ to 70$^{\circ}$, which is adopted as a plausible range based on the AGN unified model assumption, applying HLX–1~ESO 243–49, OJ~287, and 1H~0707–495 as reference scaling sources. We also estimate a BH mass in RX~J1301.9+2747 applying a timing analysis, in which the Compton cloud size to be $\sim 10^{11}$ cm, estimated from the quasi-periodic oscillation frequency, $\nu\sim 10^{-4}$ Hz, indicates SMBH mass in RX~J1301.9+2747 is of order of $10^6$ M$_{\odot}$. Overall, the BH mass obtained by the scaling method in this source is consistent with previous measurements using other methods.

We study the quantum Cayley graphs associated with the Kac-Paljutkin quantum group. We determine which projections give rise to undirected, irreflexive and connected quantum graphs and classify them up to isomorphism. Their spectra and chromatic numbers are computed. For the special case of the projection $p = I_2$ we also compute the associated quantum Cuntz-Krieger algebra.

Existing visual navigation policies are inherently bound to fixed camera configurations, creating a fundamental barrier to zero-shot deployment across heterogeneous robot sensor layouts. To overcome this limitation, we present an embodiment-informed navigation policy capable of generalizing across diverse depth sensor configurations on a specific aerial platform. Instead of implicitly learning spatial alignments, our approach explicitly unprojects depth measurements from arbitrary depth sensor payloads, varying in sensor count, mounting extrinsics, and intrinsics, into a shared robot-centric frame, stitching them into a unified spherical range image and a binary validity mask. This mask allows the downstream policy to explicitly distinguish covered space from unobserved blind spots. Trained via reinforcement learning with aggressive camera randomization, our policy generalizes zero-shot to unseen layouts featuring up to seven cameras, scaling success rates from 78% to 95% as total spatial sensing coverage increases. Finally, real-world flight trials on a physical quadrotor, conducted in an obstacle-filled corridor and an outdoor forest, validate the policy's zero-shot transfer across camera configurations and its resilience to sudden online sensor dropouts.

The COVID-19 pandemic emphasised the importance of remote emotional communication and highlighted a gap in existing technologies that lack haptic channels. While video calls maintain visual and auditory presence, they cannot convey the emotional depth of physical contact, especially hugging, a universally recognised form of intimacy and support. To explore this challenge, we developed the Hugging Suit, a pneumatically-actuated wearable system that enables users to simulate and receive remote hugs in real time. Unlike prior haptic systems that focus solely on tactile sensation, our approach integrates both technical and experiential considerations. The system integrates a programmable Air Actuator Matrix (AAM), a portable high-pressure pneumatic unit, and a fabric-based pressure sensor layer, enabling precise, wearable haptic feedback while remaining lightweight and mobile. Guided by a Research through Design (RtD) methodology, we iteratively refined the prototype to improve tactile resolution, overall usability, and user comfort, while introducing modular components to support flexible and scalable haptic configurations. In parallel, we explored how specific contextual factors, such as lighting, privacy, and the visibility of the remote partner, might shape the emotional and perceptual experience of receiving a remote hug. Preliminary feedback suggests that low-lit, private spaces, especially when users could also see their remote partner via video, improved emotional engagement and comfort during mediated haptic experiences. Our low-cost, maker-space-friendly approach contributes to affective haptics applications in long-distance relationships, emotional regulation, and remote therapeutic support.

We study the interplay between symmetry defects insertion and the phenomena of quantum many body scarring. We exploit a class of models obtained from an embedding mechanism that defines a stochastic matrix form hamiltonian, hosting zero energy many body scarred states. Such models display an interesting playground to explore the consequences of dualities, half-gauging operations and so on. We first show that inside this class of models, what are the conditions to still have scared states after defect insertion. The main result of our work is a detailed analysis of half-gauging in such chains, which introduces a non-trivial interface in our system, leading to scarred states protected by the underlying symmetries. The conclusions for half-gauged scarred systems are general and may lead to fruitful directions for higher dimension scarred physics and their robustness.

Current evaluation of multilingual Large Language Models (LLMs) rests on an implicit Translation-Isomorphism Assumption (TIA): that semantic structures across languages are congruent and mutually mappable without loss of information. We argue that this assumption is not merely violated in practice, but ill-posed in principle for a typologically identifiable class of concepts, including pragmatic markers, honorifics, and diachronically stratified terms. We formalize this failure using a usage-cloud framework, representing concepts as point sets of contextualized embeddings. We define $\alpha$-unalignability as the impossibility of any mapping that simultaneously preserves lexical faithfulness (centroid correspondence) and structural faithfulness (local neighborhood topology). We provide three layers of evidence. Behaviorally, we show that FLORES-200 translation failures are predicted by language family and resource class but not by script, and that LOBSTER reasoning scores vary by family. Mechanistically, we report a Representation-Intervention Gap (RIG) in a nine-model case study on Yami: the models' activations encode a regularity along which Yami groups with other low-resource and Austronesian languages, yet interventions on language-specific neurons show no demonstrated advantage over random masks: the regularity is visible but not usable by this intervention. Finally, we operationalize these findings into a multidimensional diagnostic profile: Cycle-Consistency, Pragmatic-Load Disagreement, Manifold-Curvature Mismatch, and RIG. We argue that collapsing cultural competence into a single scalar incentivizes "probabilistic flattening," and that recognizing the unalignable class is a precondition for AI that respects, rather than erases, cultural divergence. This suggests that multilingual alignment is not a single well-defined objective, but a set of mutually incompatible projections.

Classical growth theory places physical productivity at the center of economic growth. In modern service-based economies, however, growth increasingly means creating higher-valued products rather than increasing output quantities. This paper develops a theory of value growth based on a socially and institutionally sustained value scale. The framework unifies value creation, finance, and distribution and offers an account of major patterns in US economic history. The proposed framework is intended as a new approach to macroeconomic analysis and policy making.

The growth of the Internet of Things (IoT) has raised concerns over the privacy of data collected by resource-constrained sensing devices. Homomorphic encryption (HE) addresses this by letting a device encrypt its data once and an untrusted cloud server compute on the ciphertext without seeing the values. In practice, HE's memory and computational cost have kept it out of reach of microcontroller-class devices. Prior work, SEAL-Embedded, made this feasible using CKKS, but left three gaps: its arithmetic is entirely scalar, even on hardware with a vector instruction set; it never decrypts on the device, so the client cannot consume a result; and it does not explore BFV, whose encoding uses only integer arithmetic and decrypts exactly. We present Zeppelin, the first HE library to use an embedded vector instruction set, the first to support both encryption and decryption on an embedded device, and the first BFV implementation on MCU-class hardware. Zeppelin vectorizes the number-theoretic transform, HE's main bottleneck, for ARM's Helium extension, and includes a decryption procedure that avoids large-integer arithmetic and timing leakage of the secret key. A server-side adapter converts Zeppelin's ciphertexts into a format compatible with Microsoft SEAL, so the device handles encryption and decryption while the server performs all homomorphic computation. On an STM32N6 MCU with an ARM Cortex-M55, Zeppelin encodes and encrypts 4096 packed values in 4.76 ms (seeded symmetric, 128-bit security per the HE standard) and decrypts and decodes the result in 5.38 ms, using under 500 KB of RAM, with the vectorized NTT engine ${\sim}2.7\times$ faster than an equivalent scalar implementation on the same core.

Long-term conversational memory is becoming an integral component of modern LLM systems. Proposed architectures group records by topics and events, construct hierarchies and graphs, and connect facts through causal and temporal relations. We experimentally study the interaction between two memory parameters: structural depth and the width of context supplied to the answer model. Using EverMemBench, we evaluate depths D1-D4, core budgets of 1,024/2,048/4,096 tokens, and additional Production and Oracle conditions up to the full archive. Increasing width from 1K to 4K improves Accuracy by 10.11-17.98 percentage points, whereas increasing depth provides no monotonic gain. Beyond 8-16K, Production performance reaches a plateau while tokens per correct answer continue to increase; Oracle preserves quality on full archives of 68-71K tokens. These results motivate further investigation of large, coherent context blocks instead of progressively deeper memory structures.

Pauli decomposition of an $n$-qubit operator is expensive if each of the $4^n$ Pauli strings is treated as an unstructured object. Labeling those strings by the configuration space $(\mathbb{Z}_2)^n$ makes them displacement operators $X^{\otimes x}Z^{\otimes z}$ on the computational space: shifts by~$x$ and multiplications by characters $Z^{\otimes z}$ in the computational basis. That labeling organizes the operator into $2^n$ fibers of length $2^n$, one per shift~$x$, each collecting the computational-basis amplitudes that hop by~$x$. Expanding each fiber function in the character basis of $(\mathbb{Z}_2)^n$ — a length-$2^n$ Walsh–Hadamard transform — recovers the Pauli coefficients at total cost $O(n\cdot4^n)$. The same fiber / shift–character picture extends to $(\mathbb{Z}_p)^n$ (Heisenberg–Weyl qudits). paulikit is a memory-bounded realization for qubits: for matrix-sparse inputs, peak memory need not densify to a full $2^n\times2^n$ operator. Performance is checked on a stated low-end GNU/Linux platform for a coupled-oscillator sweep beyond a billion Pauli terms.

Physical crosslinks in conventional gels are static and spatially localised, fundamentally limiting their capacity to adapt, self-heal, or perform mechanical work. Topological gels, which are held together by physical entanglements such as threadings, links, and mechanical interlocks, constitute a different paradigm by treating connectivity as a mobile, dynamic degree of freedom. Here, by using molecular dynamics simulations of semiflexible polymers and threadable colloidal rings, we establish some general design principles that transform self-assembled topological gels into programmable soft materials. We present three different modes of control. First, by controlling the mobility of the entanglements, one can tune the mechanical response of the material. Quenched anchoring forces the network to store elastic stress and yield, whereas with annealed anchoring the material can relax stresses by redistributing its entanglements whilst preserving global connectivity. Second, by controlling the degree or type of geometric confinement, it is possible to template macroscopic architecture, converting for instance 3D isotropic gels into surface-spanning 2D nets or quasi-1D topological rings with distinct graph-spectral signatures. Third, by allowing dynamical rewiring of entanglements through polymer reconnection, the material topology can be rewritten after assembly, yielding interlocked structures dominated by simple pairwise links rather than the highly complex linked states previously observed in reconnecting flexible polymers. By establishing a direct link between microscopic entanglement dynamics and emerging mechanical function, our work offers design principles for adaptive soft metamaterials and provides insights into biological topological networks such as kinetoplast DNA and chromatin loop networks.

Teleoperation serves as the fallback solution to autonomous driving but reliable functions of the teleoperation require a certain amount of mobile network resources, which cannot be guaranteed at all times. Therefore, predictive quality of service (pQoS) is introduced as a concept to increase the resilience of the teleoperation. In this paper, based on a data measurement campaign, we propose a prediction framework to prediction two important network KPIs of teleoperation: uplink data-rate and round-trip latency. Furthermore, we introduce a method to alleviate the performance degradation of machine-learning-based prediction models on previously unseen data due to concept drift by incorporating historic data into the prediction pipeline. Additionally, we introduce the metric of critical scenario detection to evaluate the prediction performance specifically for teleoperation.

Generative models have the potential to accelerate inorganic materials discovery by enabling inverse design, but generating experimentally realisable crystals remains challenging. Oxidation states are widely used to assess the compositional validity of crystals and guide inorganic materials discovery. While existing generative models for crystals can generate materials with charge-neutral oxidation-state assignments, they poorly reproduce the distributions of oxidation states observed in synthesised materials. To address this limitation, we propose OxiGen, an oxidation-state-aware crystal diffusion model that explicitly represents oxidation states during generation. OxiGen enforces global charge neutrality by construction using a structured output layer with exact inference over a finite-state automaton. Empirically, OxiGen substantially improves oxidation-state fidelity, generates the highest rate of stable, unique, and novel crystals among evaluated methods, and maintains high compositional validity even under property conditioning.

Morphing has recently gained renewed interest with the emergence of generative models, particularly in audio and image generation. In musical sound synthesis, morphing can generate intermediate sounds between two targets, helping musicians and sound engineers explore new sounds with interesting perceptual properties. As morphing is inherently defined in perceptual terms, evaluating this task is challenging. In this work, we introduce Sobolev Distances to Ideal Morphing (SDIM), a novel objective metric to quantify the regularity of audio morphing trajectories in perceptually relevant audio embedding spaces. Leveraging a physics-based sound synthesizer, we evaluate the discriminative power of SDIM on controlled morphing trajectories with varying degrees of regularity and compare it with that of existing audio morphing metrics. Results show that, contrary to state-of-the-art metrics, the proposed metric reliably discriminates desirable trajectories from adversarial ones.

An analytic quadrupole octupole hexadecapole (QOH) axially symmetric model is used to provide a coherent framework for describing both octupole vibrations and octupole deformations in even-even nuclei. The model offers analytical solutions for the energy spectra and electric E1, E2 and E3 transition probabilities. The spectroscopic features are governed by three physically meaningful parameters: the stiffness constant $c_2$, the hexadecapole deformation parameter $\phi_{02}$, and the sextic potential parameter $\alpha$, directly linked to $\phi_{01}^{\pi}$ which represents the interplay between the quadrupole and octupole deformations for both even and odd angular momentum states. The model is applied across a broad range of nuclei including Ra, Th, Sm, Ba, U, Gd, Nd, Rn, Pu, Xe, and Ce isotopes, effectively capturing the characteristic properties of alternating parity bands. Detailed calculations of E1, E2, and E3 transition matrix elements have been performed for $^{220,222}$Rn, $^{222,224,228}$Ra, and $^{144,146}$Ba yielding results in good agreement with available experimental data.

In this paper, we investigate connections between dependence logics, viewed as a subclass of relating logics, and three-valued logics. More specifically, we identify common features of Epstein's subject-matter semantics and the variable-inclusion conditions characteristic of some infectious many-valued logics. Inspired by Del Cerro and Lugardon's sequent calculi for dependence logics, in which classical connectives are combined with connectives satisfying Epstein-style conditions, we introduce two three-valued dependence-like logics that combine classical conjunction and disjunction with infectious negation and implication. We also provide sound, complete, and cut-free bisequent calculi for these logics.

Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study simultaneous inference for local mean contrasts when the number of available diagrams is fixed. They are differences in expected weighted feature mass within $\ell_\infty$ neighborhoods at several centers and radii. We estimate these contrasts using additive landmark responses. A Gaussian multiplier bootstrap calibrates simultaneous confidence intervals while allowing unequal group covariances. The neighborhoods whose intervals exclude zero form a map with approximate family-wise error control, and selecting a subset of original intervals for display preserves their joint coverage guarantee. On the simultaneous coverage event, every reported neighborhood lies within twice its radius of the support of the mean-measure difference. A geometric result gives sufficient radius conditions for a displaced feature to produce a nonzero contrast. A comparison of sufficient detection thresholds quantifies the tradeoff between reducing the number of tested coordinates and reserving observations for an independent pilot. In simulations with 40 to 120 diagrams per class, the bands achieved 94%-98% simultaneous coverage under both the strict null and equal means with unequal covariances. In the latter setting, a permutation maximum and the pooled-t implementation of the two-stage persistence-image test of Moon and Lazar rejected in up to 32% and 26% of runs, respectively. In the fixed-budget simulations, spending a third of the observations on a pilot to choose landmarks or radii located changes less often than a prespecified grid at a single radius. On the MUTAG benchmark, the localized region concentrates on rings of fused-ring systems, an exploratory reading.

Machine-learning interatomic potentials enable large-scale atomistic simulations of vanadium alloys relevant to fusion applications, but reliable training and validation remain challenging in multicomponent systems. Here, we develop a descriptor-based DeepMD-DPA1 potential for the V-Ti-Cr system using a two-stage workflow: broad configuration sampling driven by the MatterSim foundation model followed by fine-tuning to density-functional-theory data computed with VASP. The model achieves root-mean-square errors of 9.2 meV/atom for energies and 0.23 eV/angstrom for force components. Using this potential in large-cell LAMMPS simulations, we compute Young's modulus, bulk modulus, and Poisson's ratio for V-4Ti-xCr and V-xTi-4Cr alloys at T = 300 K and T = 1073 K. We find that increasing Cr fraction increases the elastic moduli of the alloy, while increasing Ti fraction decreases them; all compositions are softer at 1073 K than at 300 K. Two-phase simulations give a melting temperature for pure V of 1950 K, in good agreement with experimental data.

We study Hodge–Tjurina numbers and the Tjurina subspectrum of isolated hypersurface singularities. We relate these invariants to Hodge ideals and microlocal $V$-filtrations and investigate their behavior under Thom–Sebastiani sums. For separated sums, we obtain a filtered defect formula and, in particular, give an affirmative answer to the question raised by Almirón concerning the Thom–Sebastiani property of the Tjurina subspectrum: it holds if and only if the Tjurina number is multiplicative. We also discuss rational sampling, spectral reconstruction, symmetry bounds, and examples illustrating the information captured and lost by integer Hodge–Tjurina data.

We derive the local pressure tensor generated by the original Rosenfeld fundamental measure theory (FMT) for hard-sphere fluids from an arbitrary infinitesimal deformation. The variation of a finite-distance FMT kernel is written via the line integrals of the local deformation gradient along the straight segment connecting its endpoints. The resulting symmetric pressure tensor consists of a local term expressed through the standard FMT weighted densities and a finite-range chord term. For a monodisperse hard-sphere fluid, differential relations between the Rosenfeld measures reduce the tensor to a closed one-body form. We demonstrate that no independent pair density or inhomogeneous Ornstein–Zernike equation is required. In the limit of homogeneous fluid the tensor reproduces the Percus–Yevick compressibility equation of state. In planar confinement the normal stress satisfies the hard-wall contact relation, the mechanical surface tension agrees with the surface excess grand potential, and the disjoining pressure agrees with the derivative of the confined grand potential with respect to slit width. The finite-range chord term extends the deformation method from local field theories to nonlocal weighted-density functionals.

We establish nonlinear stability of three-dimensional Couette flow for the incompressible Navier–Stokes equations on $\mathbb T\times\mathbb R^2$. Divergence-free perturbations satisfying $\|u_{\rm in}\|_{H^2}+\|u^\perp_{0,\rm in}\|_{\dot B^{-2}_{2,\infty}}\leq c_*\nu$ generate unique global $H^2$ solutions that remain close to Couette flow, where $u^\perp_{0,\rm in}$ denotes the streamwise average of the transverse velocity. This result retains the $O(\nu)$ stability threshold despite the absence of a spanwise spectral gap. The nonzero streamwise modes exhibit enhanced dissipation, their wall-normal component satisfies a viscosity-uniform time-integrated inviscid-damping estimate, and the transverse zero mode decays in $L^2$ at rate $(1+\nu t)^{-1}$. The endpoint space $\dot B^{-2}_{2,\infty}$ controls the transverse low frequencies, accommodates divergence-form nonlinear forcing, and is critical for linear lift-up from the wall-normal zero mode. The proof combines propagation of this endpoint norm, Fourier splitting, and a two-level roll-to-streak representation with an adaptation of the nonzero-mode framework of Wei–Zhang (CPAM, 2021).

Understanding the structural relationships among attributes in tabular data is fundamental to machine learning and pattern recognition. While functional dependency (FD) discovery has been extensively studied, scalable discovery of logical dependencies (LDs), particularly as the number of attributes and dependency order increase, remains underexplored. These dependencies capture non-deterministic, condition-specific relationships among pairwise or multiple attributes. Furthermore, existing approaches do not provide a unified framework for extracting multi-attribute LDs and FDs. To address these limitations, we propose LDTool and HLDTool for extracting and visualizing multi-attribute LDs and FDs from tabular data. LDTool extends dependency discovery beyond pairwise relationships, while HLDTool enables scalable extraction through hypergraph-guided search-space reduction. Experiments on three simulated and eleven real-world datasets demonstrate that the proposed framework extracts meaningful LDs and FDs while improving scalability. LDTool recovers the same FDs as existing FD discovery methods with lower runtime in high-dimensional feature spaces, whereas HLDTool enables dependency discovery in datasets with hundreds of features. The proposed framework provides interpretable visualizations of dependency structures and supports applications in exploratory data analysis and the quantitative evaluation of synthetic tabular data.

This paper addresses the challenge of automatic, frame-accurate event detection in table tennis videos. Current methods for estimating 3d ball trajectories and ball spin typically require that key events, such as ball-racket contacts, have already been identified in advance. This requirement makes it difficult to apply these methods to longer, unedited video recordings. To overcome this limitation, we propose EventNet, a two-stage pipeline to detect key events: (1) 2d keypoints are extracted of the upper-body poses for both players, table corners and ball center. A small keypoint transformer combines them into a compact representation that is robust to changes in viewpoint, lighting, and background clutter. (2) The temporal sequences of these frame-based representations are processed by a transformer encoder that predicts two time-to-event values for each frame, indicating how close the current frame is to the next and previous ball-racket contact. One novelty is a new, temporal cosine-like target signal. Furthermore, we introduce viewpoint augmentation via 3D reprojection and frame-rate augmentation to improve robustness and generalization. Our extensive ablation study gives deeper insights into the importance of various architectural and training aspects. Experimental results show that the proposed approach achieves an F1 score of 91.16% and a mean frame deviation between ground truth and predicted frame of 0.42 on the Latte-MV dataset and 73.08% / 1.16 on the challenging TTHQ dataset. Overall, our work demonstrates that 2d keypoint-based temporal modeling with our EventNet architecture is a promising and practical approach for automatic event detection in table tennis videos.

We extend a result by Ikeda and Suriajaya (2025) to the average number of representations of an integer as a sum of an arbitrary number $j\ge 3$ of primes. We show that the corresponding asymptotic formula holds in the general case. In the proof we use new ingredients like averages for the singular series of the generalized Goldbach problem.

Music Source Restoration (MSR) seeks to recover original, unprocessed instrument stems from mixed, mastered, and possibly degraded recordings. Unlike conventional source separation, which treats the mixture as a linear sum of clean sources, MSR must additionally invert nonlinear production effects, such as equalization and compression, and transmission-related degradations, such as codec artifacts. We propose a three-stage framework built around this distinction: (1) a mixture restoration model that addresses degradation before separation, (2) a single model that separates the restored mixture into eight target stems (vocals, guitars, keyboards, synthesizers, bass, drums, percussion, and orchestra), and (3) stem-specific restoration experts fine-tuned on the separator's own residual artifacts. Each stage improves restoration quality over the previous one on the MSR Challenge test set. We release code and models to support future research in MSR at https://github.com/theMoro/music_source_restoration.

We study a positive radial graph evolving by $V=H^\alpha+b$, with $\alpha>0$ and $b<0$, in the unit cylinder and with $u_r(1,t)=u(1,t)$. We separate finite-time continuation estimates from the time-uniform interior estimates needed for convergence of normalized translates. On existing classical intervals we prove height and gradient bounds and an explicit conversion of velocity bounds into estimates for $H$, $u_r/r$, and $u_{rr}$. We derive the correct boundary defect for comparisons with finite-slope translators. Under independent interior velocity bounds and two-sided slope trapping, we prove compactness and identify every translated limit with the cup translator. We identify the radial zero-number comparison still required to establish that trapping. Stationary caps and power-law Robin laws are included.

Relations between electroweak parameters can be measured with ever-increasing precision and a future lepton collider will require major advances in the theoretical predictions. We derive top-quark mediated four-loop QCD corrections to $\Delta r$ and $\Delta \kappa$, that is to the relations between the weak boson masses, the electroweak couplings, and the weak mixing angle. To this end, we expand the vacuum polarization functions of charged and neutral gauge bosons in $M_Z^2 \ll m_t^2$, finding a negligible truncation error after six terms. Our results imply a shift of a few hundred keV in the W boson mass, which will be numerically relevant for measurements at the FCC-ee.

We investigate a thermal transmission problem in a domain composed of a film region and a bulk region coupled through an interface where temperature continuity and heat-flux balance are imposed. The analysis addresses both the finite-thickness film configuration and the corresponding thin-film limit, with anisotropic, non-homogeneous thermal conductivity tensors. Letting the film thickness vanish directly leads to a degenerate problem due to the vanishing measure of the film region. To preserve the contribution of the film in the limit, we introduce suitable scaling assumptions for the normal heat fluxes, namely for the flux balance across the film-bulk interface and for the flux prescribed on the external boundary of the film region, together with the requirement that the volumetric source in the film be uniformly bounded with respect to the film thickness. Under these scaling assumptions, we derive a non-trivial thin-film limit formulation that takes the form of a coupled bulk-interface problem, where the effect of the collapsing film is represented through an additional balance relation posed on the interface. Well-posedness results are established for both the finite-thickness film and thin-film limit configurations, and a rigorous convergence analysis is carried out to justify the asymptotic limit. The main mathematical achievement consists in finding explicit convergence rates in suitable functional norms, relying only on the weak regularity of the finite-thickness problem due to the transmission conditions at the film interface. To complement the study, analytical solutions are derived for a simplified film-bulk geometry and are used to compare the thermal responses of the two configurations. These solutions also provide a quantitative assessment of the convergence rates established in the theoretical analysis.

We study isomorphism decision and basis construction for finite Abelian groups of known order $n$. We measure complexity by the number of additions performed in the groups and by the total running time. We give a randomized isomorphism decision algorithm that performs $\tilde O(n^{1/4})$ group additions and runs in $\tilde O(n^{1/4})$ time. This improves the $\tilde O(\sqrt n)$ upper bound of Chen and Fu and matches Bshouty $\Omega(n^{1/4})$ lower bound up to polylogarithmic factors. We also prove that finding a basis with success probability at least $2/3$ requires $\Omega(\sqrt n)$ group additions in the worst case. This matches the $\tilde O(\sqrt n)$ upper bound of Chen and Fu up to polylogarithmic factors. These results separate isomorphism decision from basis construction in finite Abelian groups: their optimal worst-case complexities are $\tilde\Theta(n^{1/4})$ and $\tilde\Theta(\sqrt n)$, respectivel

Facial affect models are trained almost entirely on adults, yet are increasingly applied to children in education, health, and developmental research. We present a controlled, multi-model audit of five AffectNet-pretrained expression models (EmoNet, EmotiEffLib, DDAMFN++, OpenFace 3.0, LibreFace) on children, across four child image datasets, the AffectNet-8 validation set, and two spontaneous child video datasets, through one shared harness. Three findings emerge. First, the child gap is model-agnostic: every architecture degrades from posed to naturalistic faces and shares the fear$\rightarrow$surprise confusion. Second, it is concentrated and corroborated across all five models: open-mouth faces (read as surprise, correlating with the AU26 jaw drop) and South-Asian children degrade systematically, with a smaller averted-gaze penalty, while closed-mouth faces, White and Black children, and direct gaze do not; the bias tracks expression morphology and specific populations, not skin tone. Third, the gap is diagnosable: a linear probe on frozen features reaches 0.75-0.91 on unseen children versus 0.48-0.66 zero-shot, so it lies largely in the classifier head, not the representation, whereas dimensional valence/arousal regression degrades sharply under domain shift. Building on this, recalibrating only the head on a little target data recovers $+0.13$ to $+0.28$ on the two largest child sets across all five models at negligible adult cost, though the gain is in-distribution and does not transfer across child collections. We will release the harness, per-sample predictions, and analysis code; the child face data stays license-locked and is never redistributed.