Papers

Let \(X=(X_1,\ldots,X_n)\) be uniform on the Boolean cube, and let \(Y\) be obtained by passing its coordinates independently through a binary symmetric channel with crossover probability \(p\). For a \(k\)-bit quantizer \(Q(X)\), reporting \(k\) input coordinates retains \(k(1-h_2(p))\) bits of information, making coordinate projections a natural quantization benchmark. For \(k=1\), this is the Courtade–Kumar conjecture: every Boolean function \(f\) satisfies \(I(f(X);Y)\leq 1-h_2(p)\), with equality for coordinate functions. We prove the conjecture in every dimension and for every crossover probability, without a balance assumption. The proof tracks the information gap relative to a coordinate as the channel correlation varies. After a monotone rearrangement, an entropy-flow identity relates the derivative of this gap to the edge boundary of the associated Boolean decision set. A sharp local entropy comparison, Fourier analysis, and logarithmic Sobolev estimates for pivotal sets imply that any positive gap must grow as the noise decreases, contradicting its nonpositive value at the noiseless endpoint. For \(k\geq8\), a coding-theoretic phenomenon emerges. We construct a shortened-Hamming-code quantizer that beats the coordinate benchmark for \(k=8\), and a direct-sum argument extends the failure to every \(k\geq8\). Thus structured coding can retain more information than coordinate selection. Exhaustive searches within several structured code families and Monte Carlo searches over random codebooks for \(2\leq k\leq7\) find that structured codebooks outperform random ones but remain below the coordinate benchmark. This motivates our conjecture that coordinate projections are optimal for \(2\leq k\leq7\).

Recent advances in Artificial Intelligence (AI)-powered Computer-Aided Diagnosis (CAD) systems have substantially improved breast cancer screening, diagnosis, and prognosis. Comparatively, postradiotherapy outcome prediction using paired longitudinal mammograms has received considerably less attention. This is largely due to the limited availability of well-annotated longitudinal datasets. Longitudinal mammograms, coupled with paired pre- and post-treatment information, provide a unique opportunity to characterize treatment-induced breast tissue changes following radiotherapy. The resulting learned representations can serve as a valuable asset for advancing personalized radiotherapy planning and post-treatment management. In this context, we propose Mammo-LIFE, a patient-level multimodal framework for post-radiotherapy outcome prediction that combines longitudinal mammographic features with patient-level clinical variables. The imaging branch processes paired pre- and post-treatment mammograms acquired from the four standard views using a mammography-specific encoder adapted via Low-Rank Adaptation (LoRA). Within each view, preand post-treatment representations are explicitly compared through a longitudinal comparison module to capture treatment-related changes. The resulting view-level embeddings are then aggregated using learned view-attention pooling to form a unified patient-level mammographic representation. Selected clinical variables are subsequently combined with the image-derived prediction probability through a late-fusion strategy. To evaluate the effectiveness of combining paired longitudinal mammograms with clinical information, experiments were conducted on an in-house clinical cohort using patient-level stratified five-fold cross-validation.

Water's anomalous properties have been hypothesized to originate from a liquid-liquid critical point in the supercooled regime, separating high- and low-density liquid states. Experimental verification remains challenging due to rapid crystallization under these conditions. A recent study reported evidence for such a transition, based primarily on a pronounced increase in the heat capacity of rapidly heated low-density amorphous ice. Here, we show that this heat capacity increase can be explained without invoking a liquid-liquid transition. By combining simulations using a machine-learning potential trained on the state-of-the-art MB-pol water model, combined with the Tool-Narayanaswamy-Moynihan (TNM) model of the glass transition, we demonstrate that the observed signal can arise instead from a dynamical effect induced by the mobilization of rotational and translational molecular degrees of freedom during ultrafast heating. We further show that our findings are fully consistent with recent electron diffraction measurements showing structural arrest of supercooled water close to our predicted glass-transition temperature. These results provide an alternative interpretation of the experimental observations and highlight the importance of nonequilibrium glassy dynamics in the interpretation of the behavior of supercooled water on ultra-short time scales.

In this paper, we prove the Brauer $A(\infty)$ condition for good non-defining primes. Consequently, we show a conjecture of Navarro on coprime actions and Brauer characters for primes larger than 3.

This paper reviews advances over the last decade in the field of computational structural reliability modelling. The discussion is focused on problems of time-variant/time-invariant reliability at the component level. Three broad classes of problems are considered: (a) time-invariant reliability problems involving static problems, (b) problems of time-variant reliability analysis for deterministically parametered dynamical systems driven by random excitations, and (c) time-variant reliability analysis of randomly parametered dynamical systems subjected to random excitations. Four classes of approaches are discussed: (a) analytical methods based on first/second order reliability analyses (for time-invariant reliability analysis) and level crossing based approaches for time-variant reliability problems, (b) methods based on importance sampling strategies (including the Girsanov transformation based method for dynamical systems), (c) particle and trajectory splitting based methods, and (d) methods that employ machine learning based tools (primarily involving development of surrogate models and active learning strategies) in tackling reliability problems. The focus of the discussions is on methodological advances, and questions related to specific applications are not addressed. The review presents critical discussions on the relative merits of alternative approaches (in terms of computational efficiency, accuracy, scalability, treatment of rare events, ability to handle geometric complexities linked to failure surface, and suitability for high-dimensional problems) and identifies several directions for future research.

We construct complete ALH hyperkähler metrics on complements of anticanonical elliptic curves with zero self-intersection in smooth rational surfaces. This answers the existence question of Filip–Tosatti, related to the picture proposed by Haskins–Hein–Nordström. Conversely, we prove that every hyperkähler ALH gravitational instanton admits, for each induced complex structure, a compactification by an anticanonical elliptic curve in a rational surface.

Appell functions are a large class of multi-variable quasi-elliptic functions, which are also instances of higher depth mock modular forms. A central aspect of these functions is their non-holomorphic modular completion. Our previous work developed Appell functions for a general positive definite lattice $\Lambda$, and expressed the non-holomorphic completion in terms of the generalized error functions $M_P$, which are integrals over a $P$-dimensional hyperplane in $\Lambda\otimes \mathbb{C}$. In this sequel, we express $M_P$ as a $P$-dimensional iterated integral of variables $w_j\in \mathbb{H}$, such that the completion of the Appell function takes the form of an iterated Eichler integral of modular forms. We apply this to the case of the root lattice of the $A_N$ Lie algebra, which is of particular interest because of their appearance in partition functions of topological twisted Yang-Mills theories.

As next-generation wireless systems migrate to high-frequency bands, extremely large-scale multiple-input multiple-output (XL-MIMO) is indispensable for combating severe path loss. However, the received path energy along the extremely large array aperture (ELAA) may exhibit spatial non-stationarity, rendering the conventional discrete Fourier transform (DFT) codebook inadequate for channel estimation (CE) due to its full-array angular representation. To address this mismatch, we propose a novel joint angle-subarray (JAS) codebook, where each codeword corresponds to an angular direction and a specific subarray. Spatially non-stationary CE is thus transformed into structured sparse support detection in the JAS domain. However, reliable support recovery remains challenging for conventional model-based methods. We therefore develop a signal processing and deep learning co-design framework, where data-driven JAS parallel support detection is followed by least-squares (LS)-based channel reconstruction. The matched filter response of each JAS grid is embedded into a high-dimensional feature vector. We then propose a Gram-attention module that incorporates the Gram matrix as a physical prior to guide feature purification, enabling the network to suppress leakage-related components while preserving support-relevant information of each grid. The purified features are passed to decoupled heads to infer the hierarchical sparse supports in the JAS domain. Finally, LS is performed over the low-dimensional dictionary constructed from the detected supports to retrieve path gains. Simulation results demonstrate that the proposed framework achieves the highest support detection F1-score and the lowest CE normalized mean square error (NMSE) among all baselines, while ablation studies verify the benefits of integrating the Gram-domain physical prior with data-driven representation learning.

Neutrino astronomy at high energies is an emerging field but still in a state of infancy. It is barely a dozen years ago that a diffuse flux of extraterrestrial neutrinos with energies in the TeV and PeV ranges was detected and even fewer that first individual sources could be identified. A new window to the universe has been opened after four decades of efforts to realize the gigantic instruments that made that breakthrough possible. This review describes the road towards the present, reviews the actual status of the field and sketches future developments.

Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.

Let $\Omega=G/\mathbb K$ be an irreducible bounded symmetric domain of rank $r$ and dimension $d.$ In this paper, we study the joint subnormality of $d$-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on $\Omega$ determined by $\mathbb K$-invariant kernels. We introduce the notion of contractive $d$-tuple associated with $\Omega$ and prove that the weighted Bergman shifts on $\Omega$ are contractive $d$-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.

The inner disk of the T Tauri star HD 143006 is inclined and casts a broad shadow on a large portion of the outer disk. We use this extraordinary geometry to study the impact of stellar ultraviolet (UV) irradiation on disk chemistry, temperature, and line formation. We present new ALMA observations of this disk in CO, $^{13}$CO, C$^{18}$O, CN, HCN, HCO$^+$, CS and C$_3$H$_2$ and combine these with previously-published data to get a rich dataset, which is modeled with ProDiMo models for the illuminated and shadowed side by including an optional inclined inner disk to partially block stellar illumination of the outer disk. The observed line flux contrasts between the illuminated and the shadowed disk sides are small. We explain this by introducing “equilibrated models” which consider a slow heating/cooling relaxation of gas parcels orbiting in and out of the shadow. We fit the radial line intensity profiles of all 14 ALMA lines for both halves of the disk, the SED beyond 20$\,\mu$m, and two ALMA continuum images, with an overall reduced $\chi$ of about 2.3, in one combined model. Line intensities only increase slightly on the illuminated side because the gas warms up slowly, although fast UV photochemistry significantly reduces the observable molecular concentrations. For the lines of N$_2$H$^+$ and CS, which probe deeper layers where the gas and dust temperatures are coupled, slow UV-desorption of ices such as NH$_3$ and H$_2$S plays a crucial role. This can result in a brightening of these lines on the shadowed side. The carbon-to-oxygen ratio in the outer disk of HD 143006 is slightly greater than one ($\sim 1.05$). The disk mass is fitted to be as low as $0.0012 M_{\odot}$, but almost equally well-fitting models with a fixed disk mass of $0.021 M_\odot$ can be obtained after re-adjusting the disk shape, dust, and gas heating/cooling parameters. (abridged)

Interactions between the planetary magnetic field of a hot Jupiter and the winds within its atmosphere are moderated by the electron and ion abundances. For a solar metallicity atmosphere at pressures between 10 and $10^{-4}$ bar, the primary sources for these charged species are expected to be the potassium and sodium atoms, and models of magnetic effects in hot Jupiter atmospheres have typically assumed that charged species exist within the atmosphere in their equilibrium abundances. In this work, we investigate the thermochemical kinetics of alkali species within a hot Jupiter atmosphere, thus allowing for the thermal ionisation fraction to depart from equilibrium, and demonstrate that quenching of ions occurs between 1 and 10 mbar. This increase in ionisation fraction on the nightside and at mid-latitudes results in stronger magnetic interaction, here modelled using the magnetic drag approximation, further slowing the jet and altering the global circulation. We additionally show that while quenching occurs, large magnetic resistivities resulting from low electron abundances continue to exist on the nightside between 10 and 100 mbar, in tension with magnetohydrodynamic models that assume horizontally uniform magnetic resistivities to simplify the explicit integration of the induction equation. At lower pressures ($\sim$ 0.1 mbar) where the electrons have become horizontally homogenised, the magnetic Reynolds number approaches or exceeds unity, signalling the breakdown of the magnetic drag approximation. We thus stress that chemical kinetics represents a dynamically important component of modelling hot Jupiter atmospheres while at the same time further complicating the treatment of magnetic effects.

Active microrheology is an effective tool to determine the rheological properties of viscous, viscoelastic, or elastic materials on microscopic length scales. The positional response of an embedded probe particle to an externally applied oscillating driving force allows to indirectly characterize the properties of the surrounding media. We aim to explore the linear and nonlinear response of probe particles in a microrheological setup of planar geometry. For this purpose, we extend the computational method of fluid particle dynamics from viscous fluid-like to viscoelastic and elastic media, including nonlinear regimes. We consider a system confined by solid walls. In this case, we validate the approach by quantifying the linear response in terms of a Jeffreys model. Increasing the amplitude of the driving force, we observe distinct nonlinear effects. They include distorted stress-strain curves and a gradual net drift of probe particles initially positioned close to a wall. This drift vanishes in the viscous fluid-like and elastic solid-like limits, but is manifest for intermediate viscoelastic systems. We further address a setup of two probe particles in the absence of walls. They experience reciprocal pairwise oscillatory forcing. Here, nonlinearities in viscoelastic systems induce a net drift gradually moving the particles further apart from each other. Comparing with real setups, our implementation of the driving force is in line with experimental setups of optical tweezers or active magnetic microrheology.

Dataset distillation (DD) compresses a large training set into a compact synthetic set while preserving downstream training utility. Although DD has been widely studied for images and recently extended to time-series forecasting, its application to human motion prediction remains largely unexplored. Human motion is high-dimensional and structurally coupled, and gradient matching (GM) in the original motion space optimizes many correlated variables without a prior on pose plausibility or temporal dynamics, which frequently yields implausible and unstable synthetic motions. To address this limitation, we propose a latent DD framework that regularizes distillation with a learned motion prior. Motions are first compressed by a residual-quantized variational autoencoder (RVQ-VAE), and distillation then updates only a learnable latent bank through the frozen quantizer and decoder. The pretrained decoder restricts synthetic motions to its output space, while residual quantization progressively refines the latent approximation across multiple codebooks and alleviates the representational bottleneck of single-stage vector quantization. Experiments on Human3.6M, CMU, and 3DPW with two prediction backbones show that the proposed framework outperforms direct GM in 27 of 30 evaluated settings and random subsets in every setting, and produces visibly more plausible synthetic motions in qualitative comparisons.

In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary $\pi$ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.

Adaptive regulation can itself perturb the state it is intended to stabilize. In replicated simulations of an adaptive agent, we compare external disturbance, persistent internally generated disturbance, and control-generated disturbance under regulation-first and disturbance-first ordering. Persistent internal disturbance produces the largest exposure and regulatory burden within the tested parameter grid. When positive controller updates generate an immediate disturbance cost, increasing that cost produces a nonmonotonic response: effective disturbance initially rises, variability across stochastic runs increases over an intermediate range, and corrective activity becomes strongly suppressed at higher costs. The results show how disturbance source and timing shape exposure and controller burden in this model. They motivate testing adaptive agents with distinct disturbance sources and assessing regulatory activity alongside exposure.

Revision-capable streaming speech-to-text translation (S2TT) can correct earlier drafts, but process rewards based on visible text may credit content later withdrawn. Persistent Delivery Optimization (PDO) assigns intermediate reward only to content that survives revisions while scoring final quality separately. With 7.49 h of task-specific FLEURS adaptation, PDO achieves the best BLEU on four of five directions and higher COMET than every external streaming baseline in all five directions. Relative to its History-SFT initialization, PDO reduces mean/P90 finalization-aware latency by 10.8%/11.3% and normalized erasure by 15.8%, while emitting at the first permitted 2-s update and improving macro BLEU. Zero-shot evaluation on Europarl-ST and CoVoST 2 confirms that these gains are not confined to the FLEURS training domain.

Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution applications. Deep learning surrogate models can reduce this cost; however, many existing approaches are restricted to steady-state prediction or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework has addressed these issues but remains limited to structured finite element (FE) meshes. To overcome this limitation, this study proposes DeepFEAv2, a deep learning surrogate framework that enables prediction of transient FEA simulations across different FE mesh topologies and element types. The main contributions of DeepFEAv2 are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by the mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) a FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset. DeepFEAv2 achieved R^2 values up to 0.99 and normalized errors as low as 0.38%. Compared with DeepFEA, it achieved up to 38.0% relative increase in R^2 and up to 87.1% reduction in normalized error. DeepFEAv2 also performed inference up to three orders of magnitude faster than traditional FEA. These results demonstrate that DeepFEAv2 can efficiently model transient FEA simulations across increasingly complex FE settings, providing a scalable surrogate framework for transient FEA.

Video world models achieve long-range temporal consistency by storing KV cache during generation, but the growing cache makes KV cache memory a major deployment bottleneck, which motivates low-bit quantization study for efficiency. Existing 2-bit KV cache quantization methods can achieve nearly lossless performance on VBench, however, when applied to video world models, we find they still cause severe temporal flickering and visual degradation. Meanwhile, deeper investigates show that Key quantization produces smaller reconstruction errors than Value, but surprisingly leads to larger output degradation. We trace this discrepancy to attention in video world models: Key perturbations can change the attention logits, and shift the temporal-spatial tokens selected by Queries. These observations motivate us to preserve attention logits and temporal-spatial token selection during KV cache quantization. To address this issue, we present QuantWM, a training-free 2-bit KV cache quantization framework for video world models. QuantWM introduces two complementary techniques to mitigate the attention shifts. Firstly, quantization-sensitivity-aware clustering (QSAC) jointly considers historical Query sensitivity and residual ranges to select INT2-friendly Key centroids, which reduces quantization errors in channels that are more critical to attention. In addition, principal-subspace attention compensation (PSAC) restores the remaining Key errors along the dominant Query subspace using low-rank projections, which provides a direct and efficient correction to stabilize attention logits. Experiments on LingBot-World-v2, HY-World 1.5, Matrix-Game-2, Longcat-Video and Causal-Forcing demonstrate that QuantWM significantly improves visual quality and temporal consistency, while outperforming existing methods across benchmarks with up to 6.20 KV cache memory compression and limited additional overhead.

The KPZ upper-tail field introduced by Liu and Zhang arises as the scaling limit of the narrow-wedge KPZ fixed point in a microscopic neighborhood of a conditioned large height. In this paper, we give a direct probabilistic identification of the upper-tail field. We identify the grounded positive-time sector with the KPZ fixed point started from the two-sided Brownian \(V\)-profile \(B_{\mathrm{ts}}(2x)-2|x|\), while the negative-time sector is represented through an explicit exponential tilt of the same evolution. The argument uses the directed-landscape variational structure and the local Brownian comparison under upper-tail conditioning. As consequences of these representations, we recover probabilistically the positive- and negative-time large-scale limits of the KPZ upper-tail field.

This paper introduces Dr-LiSA, a first-of-its-kind direct method for localizing 2D spinning radar intensity measurements in $SE(3)$ against 3D lidar maps. Radar-lidar localization combines the complementary strengths of the two sensing modalities: radar is robust to adverse weather and precipitation, while lidar provides high-fidelity 3D maps in favourable conditions. However, existing radar-lidar localization methods are restricted to planar $SE(2)$ localization and have generally fallen short of the accuracy achieved by lidar-lidar and even radar-radar systems. A key challenge is the substantial sensing-modality gap between radar and lidar, which observe and represent scene structure in fundamentally different ways. Dr-LiSA bridges this gap using a learned forward model that predicts radar measurements from a lidar submap at a candidate pose, enabling direct photometric alignment of predicted and observed radar scans in $SE(3)$. Dr-LiSA outperforms prior radar-lidar approaches in $SE(2)$ while achieving planar accuracy competitive with state-of-the-art radar-radar localization across more than 90 km of on-road data.

Detecting emotions is necessary for building systems that can accurately and adaptively interact with humans. Speech Emotion Recognition (SER) has become an important research focus to develop intelligent spoken interfaces. However, most studies predict emotions at the utterance level, ignoring the conversational context, along with the emotional flow and speaker interactions it carries. In this paper, we introduce ACERT (Averaged Contextual Emotion Representation through Time), a module that integrates a flexible-length window of conversational context to better capture emotional evolution in spoken interactions. To evaluate the robustness of this method, we conducted experiments on datasets spanning diverse emotionally expressive styles and contexts. ACERT outperforms current state-of-the-art (SOTA) approaches on IEMOCAP, establishes the first context-aware benchmark on SAFE, and obtains strong results on MELD for unweighted, class-balanced metrics. Ablation studies show that ACERT's gains come from emotional and conversational continuity, rather than from speaker identity or acoustic conditions.

We consider a dilatonic dyon black hole solution with a gravitational radius of $2 \mu$ and two charges, $Q_1$ (electric) and $Q_2$ (magnetic), within the framework of a four-dimensional gravitational model comprising one scalar field and one 2-form. The dilaton coupling constant $\lambda$ is fixed by $\lambda^2 = \frac{3}{2}$. This solution is related to the $A_2$ Toda chain. The circular orbits of null geodesics are explored, and the fifth-order polynomial master equation governing the photon sphere radius $R_0$ is analyzed. It is shown to admit a unique solution satisfying $R_0 > 2 \mu$. The circular null geodesics are proven to be unstable. Finally, the black hole shadow is examined, yielding relations for the shadow angle and the critical impact parameter.

Text-to-motion models generate plausible human motion but do not model a robot's dynamics; whole-body tracking controllers execute robot references reliably but cannot replan an infeasible one. Recent language-to-humanoid systems bridge this gap by training. We measure how much of the gap closes with no training at all, by putting the deployment controller itself in the loop. Sample-simulate-select (S$^3$) draws $N$ motions per prompt from a frozen text-to-motion model, retargets each to a Unitree G1 by direction-matching inverse kinematics, rolls all of them out under full rigid-body dynamics with the pretrained SONIC tracking policy, and keeps the candidate the policy executed best. Because the verifier is the deterministic simulator itself, S$^3$ attains the any-of-$N$ ceiling by construction; what we measure is where that ceiling lies and what falls short of it. On 200 stratified HumanML3D test prompts with $N=8$, upright execution rises from 83.5% to 89.5% and hardware-gate passes from 33 to 85; on the complete test split (4,184 prompts) it rises from 80.5% to 89.5%. A kinematic verifier that predicts falls well (AUROC 0.90) recovers only a quarter of this gain: ranking a prompt's own candidates is harder than classifying the population. What selection cannot fix is one class, prompts that lower the pelvis, which a generator trained on retargeted robot data does execute. We further score the semantic fidelity of the executed motion with the standard text-motion evaluator, with a real-mocap control that attributes the loss to the robot projection, ablate the retargeter against GMR (complementary failures: the any-of-8 ceiling rises to 95.0% over both), and execute all 177 gate-selected clips on the real G1: every one completes standing, with hardware tracking error matching simulation ($r=0.94$).

Reliability theory gives a mature language for layered systems, but its formal tools are not yet standard in frontier AI control. We apply them to Google DeepMind's defenses against rogue deployment. The same control stack can have cubic, quadratic, or linear rare-failure suppression depending on its failure domains. Birnbaum importance identifies which component improvements buy the most nominal reliability, while prevention changes the population on which recovery is demanded. These results give concrete guidance about what to separate, improve, measure, and test.

We establish global existence, decay, and scattering for sufficiently small, smooth, and localized perturbations of a constant non-vacuum equilibrium of a relativistic quantum hydrodynamic system in three space dimensions. In logarithmic-amplitude and phase variables, the equations form a semilinear system of coupled wave equations. The skew-symmetric coupling between the time derivatives cancels in the energy identity, yielding a natural derivative energy. The linearized system has two dispersion branches. At low frequencies, the slow branch exhibits Schrödinger-type dispersion, while the fast branch has a spectral gap; at high frequencies, both branches are wave-like. The main nonlinear difficulty arises from quadratic interactions with nontrivial time and space-time resonances. We show that the symbol of every active quadratic interaction contains the corresponding interaction phase as an exact factor. This structural cancellation removes the resonant denominator and allows us to eliminate the quadratic terms by a nonsingular normal-form transformation. Combining this transformation with dispersive and energy estimates, we obtain uniform-in-time bounds for the derivative energy and $\langle t\rangle^{-3/2}$ decay of the first derivatives in $L^\infty$. We further prove that the nonlinear solution scatters to a solution of the linearized system in the high-order derivative energy norm.

A Kähler structure on a real Lie algebra $\mathfrak{g}$ is a pair $(\omega, J)$ of a 2-cocycle and a complex structure on $\mathfrak{g}$ which are compatible in the sense that $J$ is skew-symmetric with respect to $\omega$. This paper investigates Kähler structures on Lie algebras, with a particular focus on the nilpotent case. We introduce an algebraic framework for the Kählerian reduction and oxidation of Lie algebras by one-dimensional and two-dimensional ideals. Our main structural result demonstrates that every indecomposable, quasi-nilpotent Kählerian nilpotent Lie algebra of dimension greater than four can be inductively reconstructed through a finite sequence of Kählerian central oxidations by planes. This reduction sequence originates from a base algebra that is either $\{0\}$, $\mathbb{R}^2$, or one admitting a strongly non-nilpotent complex structure. Moreover, if the complex structure is nilpotent, all intermediate reductions also have a nilpotent complex structure.

We present a stochastic data-driven predictive control (DPC) framework for discrete-time linear time-invariant systems subject to sub-Gaussian additive disturbances based solely on input–output data. In contrast to related methods that rely on exact disturbance data or at least sample generation for closed-loop guarantees, the proposed approach leverages a disturbance data estimate. By enforcing consistency of the disturbance data estimate with the available input–output data and system class, we first identify data-driven and provably causal subspace predictors for use in DPC. Then, we analyze statistical properties of the corresponding prediction error, yielding tightened constraints for the nominal predictions that guarantee satisfaction of chance constraints. The proposed DPC scheme comes with guarantees on recursive feasibility and conditional chance constraint satisfaction in closed-loop under standard assumptions. A numerical evaluation study demonstrates the performance of the proposed controller.

The induction region of a model wind farm is investigated experimentally as an adverse pressure gradient (APG) turbulent boundary layer problem, using hot-wire anemometry. An array of porous discs, with diameter $D=50$\,mm representing the farm, in multiple configurations across two turbulent boundary layers of different depths, with farm-present and farm-absent configurations compared throughout. The farm imposes a spatially developing adverse pressure gradient in the approach flow. Spanwise-averaged measurements reveal systematic farm-scale global blockage extending to at least $10D$ upstream in all cases. The farm-induced turbulence intensity increase, which reaches up to $7\%$ relative to the farm-absent reference for the shallowest boundary layer, is shown by cumulative variance decomposition to be carried predominantly by large-scale motions of the boundary layer, whilst the small-scale turbulence intensity is only weakly affected. This selective large-scale energisation is consistent with the outer-layer amplification driven by an adverse pressure gradient. The concentration of farm-induced turbulence energy at scales comparable to or larger than the rotor diameter has direct implications for turbine fatigue loading, preferentially exciting coherent rotor-scale load fluctuations at the frequencies most damaging under fatigue. The results establish a quantitative link between wind farm global blockage and APG boundary layer physics.