Papers

This paper addresses high-precision formation control for spacecraft operating in low Earth orbit, motivated by the requirements of future space interferometry missions such as SILVIA. The proposed approach formulates the relative dynamics within a port-Hamiltonian framework and introduces an Adaptive Boundary-layer Sliding Mode Control (AB-SMC) law to overcome the limitations of conventional SMC with constant gains. The key innovation lies in a dynamic, error-dependent adjustment of the sliding manifold, enhancing transient performance while guaranteeing high-precision trajectory tracking. Rigorous Lyapunov-based analysis establishes explicit ultimate bounds on the tracking error and ensures closed-loop stability, while extensive Monte Carlo simulations further validate the proposed AB-SMC compared to standard control approaches. Results show that AB-SMC achieves faster convergence, lower control effort, and sub-millimeter tracking accuracy, demonstrating its practical robustness and implementation feasibility in realistic, uncertain orbital environments while respecting low-thrust constraints.

Discrete gradient methods provide a structure-preserving approach to energy-consistent time integration of dissipative Hamiltonian systems. In their conventional formulation, however, they generally attain at most second-order convergence. Extending the perturbation principle previously developed for Poisson systems to the dissipative setting, we derive fourth-order average vector field discrete gradient schemes. A congruence-based completion preserves the positive semi-definiteness of the dissipation matrix, thereby guaranteeing unconditional energy dissipativity for all positive step sizes. This completion concept provides a systematic route to higher-order energy-consistent schemes. For purely dissipative systems, an alternative exponential completion is derived, together with structure-preserving rational approximations. In particular, we characterize Padé approximants that preserve positive semi-definiteness and can be incorporated into energy-associated splitting schemes. Numerical experiments on a damped physical pendulum and a dissipative Fermi–Pasta–Ulam system demonstrate the importance of the positive semi-definite completion for avoiding nonphysical numerical instabilities and capturing the correct qualitative dynamics. They further show that the proposed methods achieve the desired accuracy and energy consistency at a computational cost competitive with existing Galerkin-type approaches. Moreover, the fourth-order schemes outperform the conventional second-order discrete gradient method in computational efficiency over the considered accuracy range, despite their higher per-step cost.

Latent diffusion models now dominate medical image generation, and every such pipeline rests on a tokenizer that compresses images into the latent codes for image generation to operate on. Thereby, the tokenizer choice bounds every downstream task from reconstruction fidelity and generation quality to the representations available for downstream analysis. Yet, medical imaging pipelines routinely utilize tokenizers from natural imaging on the hypothesis that their behavior carries over. However, this is an assumption never tested in the medical imaging regime, where datasets are orders of magnitude smaller and images exhibit far lower inter-sample variance. We present a systematic evaluation of medical image tokenizers evaluating thirty configurations across ten model families on twelve datasets at three compression factors, spanning reconstruction, generation, latent geometry, downstream classification, and memorization. We find that (1) performance on image reconstruction and generation strongly correlate, unlike prior reports on natural images; (2) modern tokenizers use nearly all of their codebook entries, but still leave most of the latent space unused; (3) training-set memorization is mild and is further suppressed by stronger latent space compression; and (4) discrete quantization can largely preserve downstream classification, with lookup-free schemes being the main exception.

This study uses wall-resolved large-eddy simulations to investigate bypass transition in a flat-plate boundary layer subjected to free-stream turbulence. Two thermal configurations are considered: an adiabatic wall and a uniformly cooled wall. The plate geometry includes an elliptic leading edge and is designed for direct experimental reproduction, providing a framework for future numerical-experimental comparisons. The resolved leading edge allows direct examination of the early stages of bypass transition. Both simulations recover the classical sequence of receptivity, vortex tilting, lift-up, streak amplification, secondary instability and turbulent-spot growth. The wall-normal transport term is identified as a precursor of streak formation, while shear sheltering is quantified and linked to the frequency-dependent penetration of free-stream disturbances into the boundary layer. Wall cooling does not modify the bypass-transition mechanisms nor the onset location of transition. Instead, it generates thermal streaks alongside the velocity streaks and shifts the latter slightly closer to the wall, consistent with optimal-perturbation predictions. The velocity streaks retain similar amplitudes, growth rates and spanwise spacings in both thermal conditions. A conditional analysis reveals a pronounced asymmetry between high- and low-velocity streaks. Although breakdown is systematically observed within low-velocity streaks, the strongest pre-transitional evolution occurs within the high-velocity streak population, which undergoes significant amplification and a progressive displacement towards the wall before the onset of intermittency. These observations suggest that high-velocity streaks may actively contribute to the reorganisation of the streak field leading to secondary instability and breakdown.

Blockchains need more than post quantum single signer signatures. They need consensus profiled authentication objects with canonical bytes, priced invalid input rejection, stable transaction identifiers, hybrid downgrade resistance, public aggregation, merge semantics, accountable signer evidence, forward secure committee rotation, and light client consequences. We argue for domain specific post quantum signatures for blockchain roles, analogously to how hash function engineering produced domain specific primitives for hash table DoS and arithmetized proof systems. We formalize transaction authorization and quorum certificate requirements, instantiate them on Bitcoin, Ethereum, and a Sei Giga style high throughput BFT stress profile, and evaluate ML-DSA, SLH-DSA, Falcon/FN-DSA, HAWK, MAYO, SNOVA, UOV/QR-UOV, FAEST, SQIsign, LaBRADOR Falcon, Squirrel, Chipmunk, and DKKW/LeanSig. We find that NIST single signer signatures are necessary components, yet none of the current schemes is a sufficient drop in replacement for the signature layer of modern public blockchains. The missing object is a consensus ready post quantum signature profile, not another generic size table.

Angular-margin speaker encoders are widely used in voice conversion, yet the geometry of their classifier prototypes remains poorly understood. We analyze ECAPA-TDNN classifier prototypes as points on the unit hypersphere and characterize their organization using rotation-invariant angular statistics together with global and local effective dimensionality measures. Our analysis shows that standard training can induce angular concentration and a substantial reduction in effective dimensionality. To address this, we investigate two geometric regularization strategies (hinged Riesz log-energy and effective-dimension maximization) applied to classifier prototypes to encourage more uniform hyperspherical coverage. The resulting prototype sets exhibit higher effective dimensionality and improved isotropy, with configuration-dependent effects on speaker-recognition performance. When the corresponding ECAPA-TDNN models are used as speaker encoders for Fast-VGAN, the regularized systems also exhibit improved robustness in zero-shot voice conversion, particularly for previously unseen speakers.

Isoperimetric inequalities on the Boolean hypercube play a fundamental role in the analysis of Boolean functions. These inequalities have been established primarily for the uniform measure and for biased product measures, often through Fourier-analytic or inductive arguments. We develop a curvature-based semigroup framework to establish isoperimetric inequalities for measures with weakly dependent coordinates. In particular, we show that a Dobrushin-type condition, together with marginal boundedness of the distribution, implies the local Bobkov inequality, Talagrand's $L^1$–$L^2$ and variance–surface-area inequalities, the Kahn–Kalai–Linial inequality, and the Eldan–Gross inequality. Our results apply to zero-field Ising models with interaction matrix $J$ throughout the Dobrushin uniqueness regime $\|J\|_1<1$. The framework builds on discrete Bakry–Émery theory and gradient estimates and can also be extended to measures on Hamming slices or hypergrids.

Arm-locking is an important technique for suppressing laser frequency noise in space-based gravitational-wave detection. However, stronger noise suppression inevitably increases the magnitude of frequency pulling, thereby prolonging the lock-acquisition time and increasing the risk of system instability. To address this issue, this paper proposes a real-time Doppler-frequency measurement and frequency-pulling suppression method based on a linear-quadratic-gaussian controller. To achieve a balance between noise suppression and pulling suppression, a time-varying control strategy is adopted. At the initial stage of the time-varying control process, the primary objective is to rapidly limit frequency pulling. Subsequently, the level of pulling suppression is gradually relaxed while the capability for laser frequency-noise suppression is progressively enhanced, so that the residual frequency noise satisfies the time-delay interferometry (TDI) requirement by the end of the transition. Comprehensive performance simulations are conducted for several arm-locking configurations. The results show that the proposed suppressor can reduce frequency pulling within approximately 1000 s while limiting its magnitude to below 100 MHz, thereby eliminating the need for the conventional Doppler frequency pre-estimation stage. When a Fabry-Perot laser is used, the amplitude spectral density (ASD) of the closed-loop laser frequency noise meets the requirements of second-generation and first-generation TDI after 2000 s and 9200 s of closed-loop operation, respectively. These results demonstrate that the proposed suppressor provides both rapid frequency-pulling suppression and a high level of laser frequency-noise suppression. This new method provide a feasible way for rapid acquisition and locking of arm-locking.

Accurate attitude estimation is essential for autonomous in-orbit servicing and proximity operations. This work proposes a Recurrent Convolutional Neural Network (RCNN) used in coarse attitude initialization of known, possibly tumbling spacecraft using LiDAR-derived depth images. By processing temporal sequences of 2D point-cloud projections, the RCNN effectively handles symmetries, occlusions, and degraded sensing. Simulations across various spacecraft geometries, angular velocities, and ranges show that the RCNN yields lower initialization errors and higher convergence rates than conventional CNN baseline within the adopted experimental framework, with performance varying across angular velocity conditions.

We establish a strongly sublinear counterpart of a recent result of Chudnovsky, E S, and Lokshtanov (arXiv 2025) on treewidth and tree-independence number. Namely, we prove that a hereditary graph class has strongly sublinear tree-independence number if and only if, for every fixed clique bound, its graphs of bounded clique number have strongly sublinear treewidth. In fact, this is part of a broader equivalence theorem. For hereditary classes, these conditions are also equivalent to having clique-dependent polynomial expansion, to admitting balanced separators whose size is bounded by $K\omega(G)^s |V(G)|^{1-\beta}$ for fixed $K,s,\beta>0$, and to admitting balanced clique-based separators of strongly sublinear size (equivalently, weight). Thus, we show that all these properties, which arose independently in the study of subexponential-time exact algorithms and polynomial-time approximation schemes, in fact describe the same hereditary graph classes. As a consequence of our equivalence theorem, we also show that every hereditary class $\mathcal C$ with strongly sublinear tree-independence number admits a subexponential-time algorithm that, given $G\in\mathcal C$, computes a tree decomposition of $G$ with strongly sublinear independence number.

Score monotonicity and rank monotonicity are properties describing the behavior of a centrality measure when an arc is added to a network: the former requires that the score of the target of the arc should increase, the latter that its importance with respect to the remaining nodes should not deteriorate. While in directed networks almost all classical centrality measures satisfy both properties, in undirected networks they fail for most measures: adding an edge can reduce the score or the rank of one of its endpoints. Semi-monotonicity is a recently introduced weaker property for undirected networks, requiring that at least one of the two endpoints of the new edge enjoys monotonicity, and it is known to hold for closeness, harmonic centrality, distance-decay centralities and betweenness. In this paper we study semi-monotonicity for three classical spectral centrality measures: eigenvector centrality, Katz's index, and PageRank. We prove that all of them are strictly rank semi-monotone on connected undirected graphs, and that all of them are also score semi-monotone, (the only exception being eigenvector centrality when scores are normalized by projecting the constant vector on the dominant eigenspace, for which we provide a counterexample). In particular, adding an edge can never decrease the PageRank of both its endpoints, which answers a question left open in previous work.

Vision-Language-Action (VLA) models map observations to actions with no objective that accounts for how the world responds, so their robustness is bounded primarily by data coverage. World models carry precisely that missing objective and are better grounded for it, yet rolling the future forward costs seconds per decision and rules them out of the control loop. We show the two can be separated. What a world model knows about physical scenes lives in its internal features; generating the future is merely the objective that produced them, so the grounding can be inherited while the generative machinery is left behind. We add one feature-alignment term to ordinary VLA training: a frozen world model is run over the training frames once and cached, and the student learns to agree with that cache. No teacher is loaded during training, the projector is discarded after it, and the deployed policy is identical to the undistilled baseline, running in 32ms and 1.86GB on a consumer RTX5090, so every gain is attributable to the representation rather than to added capacity or test-time compute. A 0.8B student reaches 97.9% on LIBERO, improves from 48.2% to 50.5% on RoboCasa-GR1 humanoid manipulation, and the same objective carries over to real hardware, on both a single-arm and a bimanual platform. The gain survives changes of student scale, backbone, alignment layer, and teacher, indicating a broad representational prior rather than a fragile alignment between two particular networks. Project page: https://thaw-vla.trung-dt.com/.

We propose a kernel-based estimation framework for Multivariate Generalized Gamma convolutions (MGGC), a class of probability distributions on R d + . MGGC are useful for risk modeling e.g. Their densities are in general not explicit. The construction relies on a new Stein operator for the MGGC class, derived from a partial differential equation satisfied by the characteristic function and expressed as an integral against the underlying Thorin measure. This leads to construct a new kernel and an estimation procedure in the derived reproducing kernel Hilbert space (RKHS); with consistency results. Numerical experiments illustrate the practical behaviour of the proposed estimator.

The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of $s$-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.

We consider the recovery of low-multilinear-rank tensors from linear measurements and propose an adaptive block-weighted modewise Riemannian gradient descent method. The method combines memory-efficient modewise measurements with a normalized adaptive weighting strategy for the core and factor components of the Riemannian gradient. The weighting improves convergence without increasing the multilinear-rank bound of the search direction or the size of the reduced core used for retraction. Under the tensor restricted isometry property and a suitable initialization, we establish local linear convergence and derive sampling guarantees for sub-Gaussian and subsampled orthogonal with random sign (SORS) measurements. Numerical experiments on synthetic low-Tucker-rank tensors show that the proposed method reduces iteration counts and computational time while maintaining reliable recovery performance, especially near the recovery threshold and for structured SORS measurements.

Continual learning with Low-Rank Adapters (LoRA) typically mitigates forgetting by penalizing the overlap between a new update and the accumulated past weights, which discourages certain update directions without controlling how an update distributes its energy over the ones that remain. We ask whether that restriction has to be task-aware, or whether a generic one supplied by the optimizer is enough. We train a plain incremental LoRA (IncLoRA) with Muon, which orthogonalizes each update, and compare it against O-LoRA and ELLA over five seeds and three task orders on the Standard CL Benchmark and three seeds on TRACE. IncLoRA+Muon reaches the accuracy band of the dedicated methods on Standard CL and improves on every AdamW configuration on TRACE. One update-constraining mechanism is enough, whether it comes from the loss or from the optimizer; on Standard CL a second one does not help, and for the most restrictive method it costs 8.4 points of accuracy and the plasticity to fit each task. What separates the two optimizers is not the size of the update, which under Muon is 0.91 to 2.06 times that under AdamW, but how it is distributed. AdamW confines it to between 1.4 and 1.8 effective singular directions, Muon spreads it over 7.0, and the two do not overlap in any tracked run. Part of the advantage usually attributed to dedicated CL methods may therefore be explained by the geometry of the optimizer's updates.

Large language models (LLMs) are increasingly used to make predictions from numerical time-series histories and textual events. Yet accuracy alone cannot reveal whether correct answers reflect effective integration of the two inputs or instead arise from event polarity, unimodal priors, or superficial cues. Likewise, plausible explanations may rationalize predictions without faithfully reflecting the evidence that drives model behavior. We introduce TimeLitmus, a diagnostic benchmark for cross-modal understanding and explanation faithfulness in event-conditioned time-series prediction. TimeLitmus contains 4,856 evaluation records across Finance and Traffic, combining natural prediction with controlled counterfactual and contrastive interventions, explanation-targeted faithfulness tests, and systematic shortcut controls. Across ten representative LLMs, standard prediction accuracy substantially overstates reliable cross-modal understanding: Hard Paired Contrast (HPC) pair correctness peaks at only 19.2% in Finance and 11.7% in Traffic, and all ten models show lower-than-expected consistency on Finance series-side controls. Models often recognize scenario relations explicitly yet fail to apply them during independent prediction. Explanation faithfulness shows a similar gap: in Traffic, most models cite the manipulated temporal factor in over 90% of cases, while behavioral support remains below 22%. Human annotators outperform LLMs on matched controlled and hard-pair diagnostics, confirming that these distinctions are recoverable from the inputs. Natural-only adaptation yields selective gains in evidence selection and input sensitivity, but not consistent gains in controlled or hard-pair behavior. The benchmark, evaluation suite, and supervised adaptation data will be released publicly.

Calibrating a simulation model involves estimating its parameters by comparing model outputs with experimental data, so that simulation results faithfully reproduce the experimental observations. When the outputs are functions of time, there are multiple ways to quantify the discrepancy between experimental and simulated curves. A recent approach based on elastic functional data analysis decomposes a functional output into two components: a function temporally aligned to a template, and the corresponding warping function. This decomposition splits the problem into two independent calibration tasks, thereby addressing functional misalignment. However, it assumes that experimental and simulated curves share the same temporal support, an assumption often violated in practice when initial or end times are themselves uncertain or depend on the calibration parameters. In this work, we reinterpret the decomposition step as an approximation to a more general Bayesian calibration problem that incorporates an error term on the time axis. This perspective allows us to naturally extend the framework to a broader family of time warpings with varying initial or end times, using partial elastic alignment. We illustrate the method on a synthetic test case, comparing it with existing Bayesian calibration methods and demonstrating improved surrogate performance and error modeling. We then apply the proposed approach to the calibration of an equation of state (a thermodynamic equation relating the state variables of a material).

We determine the exact second-order asymptotics of covert communication over binary-input discrete memoryless channels when covertness is measured by variational distance. Previous work by Tahmasbi and Bloch [IEEE Trans. Inf. Theory, Apr. 2019] characterized the first-order asymptotics and derived achievability and converse bounds on the second-order term, but these bounds do not match. The gap arises from an additional penalty of order n^{1/4} in the achievability bound. We show that this penalty can be removed through a sharper analysis of the distribution of the warden's output induced by pulse-position modulation. Specifically, we express the variational distance through the Bhattacharyya coefficient of two distributions and the expectation of a continuous function of the log-likelihood ratio. Because the resulting expectation involves a continuous function rather than the probability of a likelihood-ratio event, an analysis of the characteristic function combined with a Gaussian smoothing argument reduces the approximation error from O(n^{-1/4}) (derived from the Berry–Esseen bound in prior work) to O(n^{-1/2}). With this better controlled approximation error, we manage to derive a matching achievability result to the existing converse result, thus establishing the exact second-order asymptotics.

Prompt $J/\psi$ hadroproduction poses two related puzzles: fixed-order hadronic and $e^+e^-$ analyses give incompatible constraints on the same color-octet (CO) long-distance matrix element (LDME) combination, and the weak observed polarization is difficult to reproduce together with the yield. We analyze high-$p_T$ production in the fragmentation-function formalism with leading-logarithmic threshold resummation in both nonrelativistic QCD (NRQCD) and soft-gluon factorization (SGF). Combining the resummed hadroproduction fit with bounds from resummed $e^+e^-$ production, we find in both frameworks a common LDME region satisfying the two constraints simultaneously: threshold resummation resolves the universality tension present at fixed order. There, the $^{1}S_{0}^{[8]}$ contribution is small and the yield is governed by the $^{3}S_{1}^{[8]}$ and $^{3}P_{J}^{[8]}$ channels, whose leading transverse contributions largely cancel. The cancellation amplifies spin-symmetry-breaking transitions in the $^{3}S_{1}^{[8]}$ channel, so that within a one-parameter spin-flip ansatz a contribution of natural order $v^4$ accommodates both the measured yields and the weak polarization. A similar sensitivity holds for $\psi(2S)$ production.

A key motivation for Heyting's intuitionistic logic was to gain a formal notion of Brouwer's idea of mathematics as a "construction of the mind". One might thus argue that Heyting's Calculus should also correspond to a notion of provability. Inspired by this idea, Gödel formalised this connection via an embedding into a modal calculus, which is now known as the modal logic S4. While in his original publication, he only proved soundness for the embedding from intuitionistic propositional logic into S4, the converse was proved fifteen years later by McKinsey and Tarski. Although, it was later discovered that Gödel also had obtained a proof of the faithfulness of his embedding in unpublished notes in 1941. Rasioa and Sikorski later extended Gödel's embedding to first-order intuitionistic logic. In 1954, Maehara independently obtained the same results using proof-theoretic methods, even extending the embedding to one from intuitionistic first-order logic into intuitionistic first-order modal logic. This document presents a faithful English translation of Maehara's 1954 paper.

For every admissible non-maximal Toledo invariant $t$, we construct a locus of irreducible representations of a closed genus-$g$ surface group into $\mathrm{PU}_{2,n+1}$ with Toledo invariant $t$ whose orbit maps are quasi-isometric embeddings. These loci have real codimension $10(g-1)$ or $10(g-1)+2(n-1)$ in the character variety depending on the Toledo value. Our construction uses $4$-cyclic Higgs bundles and their correspondence with $\partial$-alternating surfaces in complex pseudo-hyperbolic spaces. The associated equivariant minimal maps into the symmetric space are bi-Lipschitz embeddings. We further construct cocompact domains of discontinuity in the Shilov boundary. Their quotients are smooth fiber bundles over the surface with fiber homeomorphic to $S^{2n-1}\times S^{2n-1}$.

We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.

The Wigner entropy conjecture posits that pure Gaussian states minimize the Shannon entropy of non-negative Wigner functions, known as the Wigner entropy. We show that mixing a specific pure Wigner-negative state with another suitably chosen quantum state can restore Wigner positivity while retaining a Wigner entropy that is slightly - but strictly - below the vacuum entropy. As a consequence, we disprove the Wigner entropy conjecture, as well as the stronger Wigner majorization conjecture, by deriving simple analytical counterexamples with violations of the entropy bound no larger than $10^{-3}$. Such states with sub-vacuum Wigner entropy can be found arbitrarily close to the vacuum and can also exhibit sub-vacuum Wigner-Rényi $\alpha$-entropy for $0<\alpha<2$. We identify the physical mechanism behind the existence of such states, which arises from a subtle interplay between the uncertainty principle and non-Gaussianity. The key idea of this paper was developed with the help of AI tools, building on the characterization of extreme non-negative Wigner functions.

Providing autonomous intelligence, pervasive connectivity and usability to human life and industry has led to the emergence of the Internet of Things (IoT). To support time-sensitive and resource-constrained applications, IoT systems nowadays increasingly rely on edge computing. This brings computation and decision-making closer to end devices. In edge-enabled IoT architecture, latency and communication overhead are reduced, but interactions among a larger and more diverse set of devices, edge nodes, services, and data sources are introduced as well. In such environments, security and privacy mechanisms provide the foundation for protection, while trust management can assess the reliability of interacting entities and adapting secure decisions. In this paper, we systematically review the current state of trust management in edge-enabled IoT. To this end, we propose a comprehensive taxonomy that maps physical, network, and application architectural IoT layers against the consumer, commercial, industrial, and infrastructure IoT domains. We further investigate state-of-art research based on their trust design, how trust integrated into secure IoT operations, the attacks that effect trust management process. Based on these findings, we identify key gaps in current research and outline future directions for context-aware and adaptive trust management in edge-enabled IoT.

Reliable uncertainty estimation is essential for deploying object detectors in autonomous systems operating in uncertain environments. Evidential Deep Learning (EDL) provides a principled framework for uncertainty-aware classification by representing network outputs as evidence and interpreting predictions through subjective logic. However, existing evidential object detectors typically combine evidential classification with regression uncertainty models that do not share the same theoretical foundation. In this work, we propose an evidential version of YOLOv8 in which both classification and bounding-box regression are formulated within a common evidential framework. Our approach exploits YOLOv8's distribution-based bounding-box representation, allowing the evidential formulation to be applied not only to classification but also to localisation. As a result, both tasks produce belief, uncertainty, and probability estimates that can be interpreted within the Dempster–Shafer framework. Experiments on KITTI, MUSES, and nuScenes show that the resulting detector remains broadly competitive with standard YOLOv8 in terms of detection accuracy while providing a localisation uncertainty that effectively discriminates between correct and erroneous detections. Moreover, this uncertainty becomes increasingly discriminative under domain shift.

We compute an explicit contribution of supercuspidal representations arising from Yu's construction to the middle étale cohomology of local Shimura varieties. For the proof, we construct special affinoids in local Shimura varieties whose reductions are isomorphic to Heisenberg Deligne-Lusztig varieties and then apply positive-depth Deligne-Lusztig theory. Along the way, we propose a stacky analogue of special affinoids using the stack of local shtukas and observe that the `general canonical subgroup problem' can be solved purely on the stack of local shtukas, which yields the corresponding claim on Shimura varieties via the Hodge-Tate period map.

Quantum machine learning is a promising paradigm for learning from limited data, a central bottleneck in domains such as medical imaging, clinical trials, and rare diseases. Quantum convolutional neural networks (QCNNs) are particularly attractive in this setting, combining a hierarchical architecture with strong inductive bias and a parameter count that grows only logarithmically with system size. Their appeal rests on the generalization bounds of Caro et al. (2022), which show that the generalization error of a quantum model scales with the number of trainable parameters rather than with the Hilbert-space dimension, placing QCNNs in a potentially sample-efficient regime. We develop a hardware-compatible QCNN with mid-circuit measurement and classical feed-forward, and show on a binary handwritten-digit task that strong test performance is achievable from as few as 10 training samples, with the generalization error decreasing as the training set grows. At a matched 45-parameter budget the QCNN learns where an equally small classical convolutional network stays at chance, although an unconstrained classical baseline with roughly 25,000 parameters remains strongest when data are plentiful. Transpiling amplitude and angle encoded circuits across image resolutions from 2x2 to 512x512 pixels then exposes the dominant scaling bottleneck: amplitude encoding stays qubit-efficient but grows extremely deep, whereas angle encoding stays shallow but becomes qubit-prohibitive. On the medically motivated BreastMNIST benchmark the QCNN does not surpass the unconstrained classical network, yet it learns consistently above chance using orders of magnitude fewer parameters. Our results indicate that for QCNNs, learning from few samples is attainable in practice, whereas scaling to realistic image data is constrained less by optimization than by data encoding and hardware execution.

We study arithmetic operations and maps which preserve normality. Revisiting a recent argument of Dayan, Ganguly and Weiss, we give a streamlined, self-contained presentation of the probabilistic proof that the non-zero rationals are exactly the multiplicative normality preserving numbers in a fixed integer base. We also include the extension to all bases simultaneously, using the theorem of Hochman and Shmerkin. In the additive case, we extend Rauzy's characterization of deterministic numbers in a fixed integer base to absolutely normal numbers. Namely, a translation preserves absolute normality if and only if its parameter is deterministic in every integer base. We prove this extension by a sparse random perturbation argument. Finally, we show that all locally $C^2$ normality preserving maps need to be affine-linear. The regularity assumption cannot be weakened to $C^{1,1}$: we construct a non-affine $C^{1,1}$ diffeomorphism which preserves normality in every integer base, and hence absolute normality.

As low-altitude applications expand across emergency response, intelligent transportation, and autonomous operations, they demand communication networks that can deliver flexible, resilient, and rapidly deployable connectivity. Heterogeneous UAV networks are a promising solution, as they can dynamically provide sensing, access, relay, and backhaul functions. Yet, most existing approaches assume predefined missions, prior knowledge of user distributions, and manually configured infrastructure, making them ill suited to dynamic and initially unknown environments. Addressing this limitation requires a shift from mission-oriented UAV deployment to autonomous network formation, in which UAVs continuously perceive their surroundings, infer evolving service demands, and self-organize network resources. Agentic AI, empowered by large language models (LLMs), offers a new foundation for this shift by integrating closed-loop perception, reasoning, planning, and execution across heterogeneous information sources. Unlike conventional optimization and learning methods designed for individual networking tasks, agentic AI can coordinate these capabilities to support sustained, network-level autonomy. In this article, we explore agentic AI for autonomous and self-organizing heterogeneous UAV networks in low-altitude environments. Our key contribution is an LLM-assisted architecture in which a base-station-hosted agent conducts global network reasoning and autonomously reconfigures access and backhaul infrastructure. The proposed system explores unknown environments, discovers users, and deploys UAVs on demand to provide access and establish end-to-end backhaul connectivity. A case study illustrates how this agentic-AI-driven approach can transform UAVs from task-specific platforms into a continuously evolving communication network.