Papers

Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural networks model images as regular Euclidean grids, limiting their ability to preserve geometric relationships and higher-order structural information. Recently, manifold topological deep learning (MTDL) has emerged as a promising paradigm that integrates deep learning with geometric and topological representations. Nevertheless, existing methods have not yet fully exploited discrete manifold structures within combinatorial complex neural networks. To bridge this gap, we introduce CNMTDL, a MTDL framework that integrates Hodge decomposition with a combinatorial attention mechanism. In our approach, medical images are represented as discrete manifolds and decomposed into three Hodge components. Features extracted from these components are concatenated and embedded into a combinatorial complex architecture, enabling enhanced higher-order message passing between $0$-cells and $2$-cells through attention-based blocks. We evaluate CNMTDL on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.

In this paper, we study the diversification properties of convex combinations of iid infinitely divisible random variables. For Lévy processes with bounded variation sample paths, we characterize, in terms of subadditivity and concavity of the transformed Lévy tails, Lévy processes that exhibit the non-diversification phenomenon or the reverse diversification order with respect to the majorization order uniformly over all time horizons. For general symmetric Lévy processes without a Gaussian component, we show that the symmetric 1-stable Lévy process is the only nontrivial process exhibiting either phenomenon. We further investigate convex combinations of components of multivariate infinitely divisible distributions, allowing for dependent and heterogeneous components, and characterize the Lévy measures of multidimensional Lévy processes exhibiting the two adverse diversification phenomena uniformly over all time horizons. Explicit characterizations are obtained for the multidimensional symmetric Lévy processes, multidimensional $\alpha$-stable processes and multidimensional compound Poisson processes. Finally, we show that the non-diversification phenomenon extends beyond Lévy processes to running maxima and integrals of increasing convex functionals of Lévy processes, while both adverse diversification phenomena are preserved for Lévy-driven stochastic integrals with nonnegative deterministic kernels. Applications to ruin theory, storage processes and stochastic volatility are also discussed.

Large language model (LLM) inference replicas run across tightly coupled GPUs and serve traffic continuously for weeks. Hardware and software failures are therefore inevitable, and one worker failure can disrupt an entire replica. Recovery requires reinitializing the engine, taking minutes even when weights and compilation artifacts are cached. Production deployments overprovision serving capacity to mask this window. We argue that the dominant cost is loss of ready serving capacity, not request progress, so recovery should preserve initialized engine state rather than reconstruct it. We present fast recovery for Dynamo based on this principle. Snapshots capture an initialized engine once and restore it instead of reinitializing it. Analysis of 18 weeks of failures from the Dynamo cluster shows that most failures are device-preserving: the engine process fails while the GPU and its resident allocations remain intact. Our key insight is that independent engine processes can reuse the same GPU-resident state while keeping mutable execution state private. The GPU Memory Service (GMS) decouples device-memory ownership from engine processes, enabling engines to share and reattach surviving allocations without copying them. GMS preserves model weights and shares them read-only between replacement and Shadow Engines, avoiding weight reloads. A second initialized runtime on the same GPUs reduces recovery to promotion. Across four models on vLLM and SGLang, these mechanisms recover a failed replica in under 7 seconds, 13-29 times faster than a warm restart, using a fixed 4-8 GiB of device memory per GPU independent of model size. Replaying the production trace, we estimate they would reclaim 79% of GPU-hours lost to recovery.

Depth-conditioned locomotion policies have demonstrated impressive agile maneuvers, but can be steered to unpredictable actions when observations are outside their training distribution. Occlusion, invalid returns, sensor noise, and visual distractors can shift deployment observations away from nominal simulated depth. While synthetic sensor augmentation targets specified degradations, it does not by itself define behavior under corruption families omitted from training. To address gaps in training-time coverage, we present REDACT (Retaining Evidence Despite Artifacts for Continued Traversal), a teacher-student framework combining an improved visual encoder architecture, persistent feature masking, and a novel consensus-gating algorithm to retain useful depth information under unmodeled corruption. The gate uses approximate conformal calibration on clean observations alone, requiring no prior knowledge of the corruption type. Trained on clean simulated depth, REDACT retains useful visual information under unseen corruption, supporting higher traversal success than existing parkour baselines. Evaluation of depth augmentation across corruption families further shows that REDACT improves robustness where augmentation coverage is missing. Real-world trials demonstrate zero-shot transfer to structured and forested environments with unfamiliar scene content.

Following a program outlined by Bartnik, and also employing nonlinear potential techniques we developed in the last years, we study lightlike singularities of variational solutions to the prescribed Lorentzian mean curvature equation with possibly unbounded (rough) curvature. This corresponds to allowing for unbounded charges in the Born-Infeld model.

We study the (Haar) measure of verbal sets in profinite groups, and especially in free profinite groups. Relating the measure of a verbal set with the width of the corresponding word, we find verbal sets of positive measure different from one. We prove a sufficient condition for the measure of a verbal set to be zero in a free profinite group of finite rank, from which we deduce that certain existentially definable sets in free profinite groups of finite rank can only have measure zero or one. Finally, we compute the measure of definable sets in torsion-free finitely generated abelian groups.

We study what LLMs do when a user applies pressure in an uncomfortable situation: a user insists, begs, flatters or grieves, and the model gives up a correct fact, writes a document it should refuse, or cheers a plan that will cost the user money, a multi-turn form of sycophancy. We send frozen multi-turn scenes to 60 models from 13 vendors and label each transcript with a trajectory (the model held its position or folded) and a manner (how it held or folded). Three scenes were used to build the codebook; six more were written afterwards and preregistered as a replication. Whether a model holds tracks its generation: fold rate correlates with a public capability index at Spearman -0.64 to -0.69 across the two scene sets, so newer models fold less, unlike earlier reports that sycophancy grows with model scale. How a model holds tracks the vendor: six of the 17 manner codes sort by vendor at permutation p <= 0.001, corrected across the codebook, and four do so again on the replication scenes. Anthropic's models name the feeling, warn and offer an alternative; OpenAI's do less of all three and almost never cite their own rules; Google's cite themselves and their AI nature when asked to do something; Meta's write the artifact they shouldn't. Six LLM coders from three vendors labeled every transcript, and three human coders labeled fifty held-out transcripts. The machines were the more consistent readers (Krippendorff's alpha 0.66 against 0.46), agreed with the author on trajectory at kappa 0.84 to 0.91, and matched the adjudicated reference at 0.83. For behavior a non-specialist can judge, the human contribution is authoring and bounding the codes and owning a small reference, not producing labels at volume.

For a positive integer $t$, let $d_t$ denote the natural density of the set of $n$ for which $t$ is a sum of distinct divisors of $n$. Erdős proved that $d_t$ exists, gave an unspecified polylogarithmic upper bound, asserted without proof a matching lower bound, and asked whether $d_t \sim c_3/(\log t)^{c_4}$. We record the explicit bounds \[ \nu_t \le d_t \ll \frac{(\log\log t)^{\delta-3/2}}{(\log t)^{\delta}}, \qquad \nu_t = \frac{K}{\log t}\Bigl(1 + O\Bigl(\frac{\log\log t}{\log t}\Bigr)\Bigr), \] where $\delta = 0.086071\ldots$ is the Erdős–Ford–Tenenbaum constant, $K=c\,e^{-\gamma}$, and $c=1.33607\ldots$ is the practical-number constant. Consequently, if Erdős's asymptotic holds, then $\delta<c_4\le 1$. A two-prime construction, using a half-scale sumset to obtain full residue coverage, then yields the pointwise excess \[ \liminf_{t\to\infty}(\log t)\,(d_t-\nu_t) \ge KI, \] where $I=\int_0^2 G(w)\,\mathrm{d}w=0.05887\ldots$ is an explicit elementary integral. In particular $d_t\ge 0.79/\log t$ for every sufficiently large $t$, and $d_t$ is not asymptotic to $K/\log t$.

We introduce back stable standard elementary monomials and their complete homogeneous analogues. These families form bases of the back stable Schubert ring and record the eventual standard elementary monomial expansions of left-stabilized Schubert polynomials. Dynkin reversal exchanges the two bases while preserving their coefficients. We also show that orbit sums of the back stable coefficients recover the elementary and complete homogeneous coefficients of Stanley symmetric functions. Finally, we study the shifted specialization polynomial $\mathcal{T}_w(t)=\mathfrak{S}_{1^t\times w}(1)$, considered by Fomin and Kirillov, which counts reduced pipe dreams of $1^t\times w$. We express this polynomial in terms of back stable standard elementary monomial coefficients.

This work studies prediction parameterization for stochastic generative dynamics in diffusion models. Existing velocity-based generative models provide the simplicity of learning a single transport field, but their standard formulation is deterministic, whereas stochastic extensions generally require additional score information or an intermediate velocity-to-score reconstruction. To retain single-field prediction while directly supporting stochastic reverse dynamics, this paper introduces Mean Velocity Matching (MVM). MVM constructs a Gaussian perturbation process for which the conditional expectation of a restoration-oriented velocity, $(x_0-x_t)/t$, directly forms the reverse-SDE drift. Consequently, a single learned field is sufficient to parameterize the stochastic reverse process without separately estimating or reconstructing the score. Because direct regression of this velocity becomes unbounded near $t=0$, MVM further introduces a $\sqrt{t}$-scaled parameterization that preserves the reverse dynamics while yielding a bounded training target. The same learned field also induces a deterministic probability-flow ODE, enabling stochastic and deterministic sampling to be studied within a unified formulation. Experiments with Transformer-based generative models achieve an FID of $\MVMImageNetThirtyTwoFID$ at \MVMImageNetThirtyTwoNFE\ NFE on ImageNet $32\times32$ and $\MVMImageNetTwoFiftySixFID$ at \MVMImageNetTwoFiftySixNFE\ NFE on ImageNet $256\times256$. Controlled SDE–ODE comparisons further show that the ODE performs better under very low NFE, whereas the stochastic reverse process achieves lower FID when sufficient function evaluations are available. These results demonstrate that MVM provides a direct single-field parameterization of stochastic reverse dynamics while maintaining competitive generation quality.

Moving authorization earlier can shorten an agent's dispatch boundary without removing authorization work. It can also admit an action whose payload, authority, or relevant state has changed. ZeroGate separates exact-action approval from durable local admission: an issuer signs a short-lived ActionPass, and a trusted runtime adapter reconstructs the final action before a local gate checks its binding and consumes its nonce. A SQLite transaction couples nonce consumption, applicable quota updates, and an admission receipt. We state a conditional decision-preservation proposition: successful local admission implies that a specified synchronous policy would authorize the same action at the admission point, provided approval is sound, all policy dependencies are represented and current, observations are faithful, and consumption is atomic. The implementation alone establishes neither current-world freshness nor exactly-once remote effects. Evaluation separates authored semantic fixtures, controlled concurrency and crash experiments, and an Azure Blob study comparing synchronous and prepared execution through the same issuer and gate. Both modes mint an exact-action pass; lifecycle latency includes preparation and prepared-batch dwell. Across 4800 cloud attempts, prepared worker-admission-to-dispatch p95 ranges from 9.802 to 11.374 ms, versus 25.018 to 334.000 ms synchronously, across the tested concurrency levels. Prepared mean complete lifecycle is longer at every level: the boundary improvement is not a net speedup. The contribution is an explicit revalidation contract, a durable reference boundary, and an auditable comparison of where authorization cost is paid, not a new cryptographic primitive or a universal performance frontier.

Weight transfer - the propagation of updated parameters from trainers to rollout generators - is becoming an important performance bottleneck in reinforcement learning (RL) systems for LLMs. The central challenge is supporting the diverse trainer and rollout layouts and synchronization requirements of modern RL workloads without sacrificing efficiency. Existing solutions are efficient under some configurations but perform poorly or lack support under others. We present WeightBridge, a flexible, efficient weight-transfer library designed to deliver high performance across diverse RL configurations. WeightBridge first automatically extracts the correspondence between trainer and rollout weight layouts, then plans and executes redundancy-free and load-balanced weight transfer. It exposes a small, general API while coordinating workers across diverse synchronization modes. Across configurations spanning different models, parallelization layouts, and synchronization modes, WeightBridge reduces average GPU stall time by up to 42$\times$ over the state-of-the-art open-source RL framework and achieves high performance in all settings. A coding agent was able to integrate WeightBridge into two different RL frameworks without manual guidance, demonstrating the generality and ease of use of its APIs.

Legal argument mining supports passage classification, retrieval, and argument completion. This work introduces an expert-annotated dataset of 42 U.S. federal tax opinions on corporate reorganizations under I.R.C. {\S}368. To our knowledge, it is the first expert-annotated, tree-structured argument corpus for this domain. Explicit spans receive one of five functional labels: Rule, Analysis, Conclusion, Background Facts, and Procedural History. Rule, Analysis, and Conclusion spans can be linked into directed support trees, while Background Facts and Procedural History serve a contextual function. The corpus provides span-based, sentence-based, flat, and tree-structured representations. Agreement analysis shows that functional node labels are more reliable than directed support edges and implicit intermediate conclusions. Directed-path agreement is stronger than direct-edge agreement, which indicates that broad reachability is more stable than exact local decomposition. Classification experiments show that functional labels are learnable under case-disjoint evaluation. Retrieval experiments show that supervised fine-tuning improves within-case retrieval. However, cross-case generalization remains weak. The dataset supports legal passage classification and provides a conservative benchmark for structured argument mining in U.S. federal tax case law.

Near flutter, modal frequency can be well resolved from accumulated phase while the sign of a small modal growth rate remains uncertain because the response envelope changes only weakly over a finite record. This work tests whether a validated physical relation between frequency and damping can exploit the better-resolved phase information to improve near-flutter stability identification. A coupling-audited SU2 Euler campaign for a modified Isogai-parameterized NACA 64A010 section at Mach 0.85 is subjected to systematic grid and temporal verification, multichannel critical-pole tracking, bootstrap trajectory closure, finite-record information analysis, and nonlinear Monte Carlo validation. The temporal study shows that 50 steps per structural period predict the wrong damping sign although frequency is already close to the finer solutions. The verified critical trajectory gives a flutter-speed index of 0.537665 and a local frequency-to-damping slope of 3.754. Restricting a free pole estimate to this trajectory gives an approximately 3.89-fold damping-precision gain, reproduced by Monte Carlo with a median RMSE gain of 3.915. At a representative operating offset and 30 dB amplitude SNR, the minimum tested record exceeding 95% correct-sign probability decreases from 15 to 5 cycles. Physically validated pole trajectories can therefore substantially reduce the observation time required for reliable near-boundary aeroelastic stability identification.

Movable antenna (MA) systems improve the channel by repositioning antennas, but each repositioning interrupts data transmission for a time set by the largest displacement and consumes actuator energy that accumulates over all displacements. Existing designs optimize the positions within a single transmission block, whereas the movement energy is limited over the long term and the positions chosen in one slot constrain those reachable in the next. We study online throughput maximization under the movement delay and a long-term energy budget. Using the Lyapunov drift-plus-penalty framework, we convert the long-term problem into per-slot problems and solve each by a proximal minorization-maximization algorithm that requires no channel statistics and keeps an antenna stationary whenever its relocation is not worth the energy. We prove that the budget is met for every channel realization and that the algorithm attains, within a controllable penalty, the throughput gain of reallocating the budget over time. Simulations show that this reallocation improves the throughput over imposing the budget slot by slot when the demand for repositioning is concentrated in time, whereas the latter, supported by the same solver, is preferable when the channel varies continuously, at the cost of an order of magnitude more antenna actuation.

Diverse pretraining has been shown to be an effective method for learning reusable, domain-aware representations that provide a starting point for fine-tuning on downstream tasks. While much of the excitement in AI for math has been concentrated in the use of frontier reasoning models to solve well-specified problems through the medium of language, narrow, specialized models remain an important component of the AI for math ecosystem. In contrast to large language models, specialized models are usually trained directly on the mathematical objects themselves (e.g., graphs, sequences of numbers) rather than the textual descriptions that characterize these objects. However, the common practice of training specialists from scratch may limit their ability to develop domain-aware representations that capture the multifaceted nature of mathematics. In this paper, we describe an approach to pretraining for permutation-focused tasks in algebraic combinatorics. We introduce PermuFormer, an autoregressive transformer trained on a 2.8 billion token multi-task, multi-encoding corpus. We show that PermuFormer is an effective starting point for fine-tuning on basic tasks unseen during pretraining and more complex research-level tasks, frequently outperforming the same architecture trained from scratch, baseline MLPs, and a fine-tuned generic language model of comparable size. We also analyze some of the internal mechanisms by which PermuFormer learns to solve training tasks. For example, we show that while some tasks can be linearly decoded directly from the internal representation of the prompt, other tasks require multiple rounds of generation before the answer can be decoded.

Data centers are being developed at an unprecedented pace, yet their energy and water impacts, and the spatial and temporal distribution of these impacts, remain poorly characterized. Data centers consume water for cooling (direct) and through electricity generation (indirect). Decisions on siting and cooling technology result in water-energy trade-offs that extend impacts beyond the facility's location. Existing assessment frameworks rely on facility efficiency metrics and average grid water intensity factors, suppressing the temporal impacts of data center load and generation availability. They also attribute indirect consumption to the facility's location rather than to the generators (and corresponding hydrologic regions) that respond to the added load, misattributing spatial impacts. To close this gap, we develop a computational model of the data center-energy-water nexus that links facility cooling and electricity demand with hourly economic dispatch, generator-level water consumption, and monthly subbasin depletion. Built on open-source data, the model resolves where and when water is consumed, and where this consumption compounds existing water risk or creates new risk. Using the model, we study different cooling configurations and proposed developments in the state of Michigan. Air-cooled data centers halve total water consumption relative to evaporative cooling, but increase electricity demand and raise indirect water consumption by one-third, shifting the water footprint from the facility to generators. Mapping these changes to subbasins reveals depletion increases beyond the data center sites, in regions that facility-level reporting may overlook. These results show that data center water and energy impacts cannot be assessed in isolation, motivating the need for integrated modeling to inform siting, design, and reporting practices.

Somatic membrane potential is the primary determinant of neuronal output, yet it remains inaccessible in many experimental setups where only dendritic recordings are available. Reconstructing somatic dynamics from distal measurements is a challenging inverse problem, particularly when the soma and dendrites are weakly coupled, as dendritic signals represent a filtered and attenuated version of somatic activity. To address this, we use a physics-informed neural network (PINN) constrained by a two-compartment Hodgkin–Huxley model. The network is trained on dense dendritic voltage recordings and the known injected current, complemented by a small number of somatic voltage samples (at most 5% of the time points), and it reconstructs the full somatic trajectory while adjusting a selected set of somatic maximal conductances. On synthetic data from four stimulation protocols, we quantify how the reconstruction depends on the amount of somatic supervision. Without somatic samples, the present formulation returns a smooth trajectory in which the action potentials are absent and the subthreshold level is biased, with a root-mean-square error of 10–14~mV; 1% of the somatic time points is enough to recover every spike; and 5% brings the root-mean-square error to about 2~mV, spikes included, with relative errors below 0.1% on the sodium and delayed-rectifier conductances. We also compare the PINN with an unscented Kalman filter constrained by the same model and assimilating the same observations, and we assess robustness to measurement noise and to random initialization. The reconstructions reported here therefore rely on sparse somatic anchoring in addition to the dendritic recordings. The results delimit what can be inferred in this synthetic, weakly supervised two-compartment setting and identify the amount of somatic information required by the present formulation.

For every infinite-type surface with an isolated puncture that admits a shift map and every natural number $n$, we study an intrinsically infinite-type mapping class $g_n$ and a simple closed curve whose orbit under $g_n$ splits into $n$ subsequences, each of which converges in the coarse Chabauty topology to a geodesic lamination on the surface. These laminations are cyclically permuted by $g_n$, and their union is a $g_n$–invariant geodesic lamination. We further show the attracting limit point of $g_n$ in the boundary of the relative arc graph has weight $n$. In particular, intrinsically infinite-type loxodromic isometries of the relative arc graph realize every finite weight.

Reconfigurable photonic interconnects are emerging as a promising communication architecture for next-generation distributed computing. Yet, most circuit schedulers are designed around an idealized view of the interconnect as either blocking or strictly non-blocking. Practical scalable designs are often rearrangeably non-blocking (RNB), with connections routed through networks of internal $2\times2$ switches. This changes the scheduling problem fundamentally: establishing a new connection can force existing connections to be rerouted, trigger state changes across multiple internal switches, and impose reconfiguration delay on otherwise unrelated traffic. We present Tetris, a circuit scheduling algorithm for RNB photonic interconnects. Tetris builds on two observations. First, All-to-All demands are often not doubly stochastic, leaving a small number of endpoints as communication bottlenecks. Second, reconfiguration delay can be large enough to change which connection should be scheduled next. Tetris prioritizes bottleneck endpoints using their remaining communication and reconfiguration work, while selecting and routing matchings to preserve ongoing connections whenever possible. Matchings ensure progress, but connections are scheduled independently, allowing completed connections to be replaced without matching-wide barriers and incurring delay only at switches whose states change. Our simulation and hardware-emulation results show that Tetris reduces All-to-All demand completion time by up to $6.6$x over Birkhoff–von Neumann-based scheduling and by $30$% over Sunflow. More broadly, RNB interconnects raise new questions in multi-tenant scheduling and routing for partial reconfiguration, which we discuss at the end of the paper.

Modern production-scale recommender systems rely on complex, multi-task ranking models. Introducing new prediction tasks into these massive systems often causes bottlenecks - it risks negative task conflicts with existing tasks, and can lead to long development and experimentation cycles due to the expensive retraining of backbone models and downstream models or tuning of reward combination formulas. To address the critical challenge of slow experimentation velocity, we introduce the Lightweight Ranking Heads (Light Heads) framework. Designed for continuous online learning environments, Light Heads enable the dynamic injection of new tasks into existing multi-task ranking models, effectively obviating the need for model cold-starting and retraining of backbone models. By utilizing stop-gradients and stateless daily training, this design strictly isolates new tasks, mitigating the risk of adverse task conflicts. Crucially, this framework uses a centralized configuration that allows Light Heads to be added to multiple models simultaneously, unblocking faster training data generation and co-training of downstream models. Successfully deployed at YouTube scale, this approach reduces the iteration cycle for multi-task experimentation from several weeks to days. In this paper, we detail the system architecture, analyze the training dynamics of stateless cold-started heads, compare their performance to full heads, and demonstrate how Light Heads have enabled the rapid A/B experimentation and deployment of new ranking tasks that yield measurable production value.

Because significant action to counter global warming requires massive public support, it is important to understand the dynamics of public opinion on climate issues. Of special interest are social tipping points, as revealed by large-scale effects of small perturbations in individual behaviors. Agent-based models (ABM) are an effective computational tool for studying these matters, because they allow controlled and systematic exploration of the effects of interventions that may be infeasible in real-world social systems. Large language models (LLMs) have been used to endow model agents with the ability to communicate in natural language (rather than by exchanging predefined messages), as well as with personality (in the form of a narrative self and episodic memory). We leverage LLM-powered ABM to look for tipping points in the social dynamics of a micro-society in which some of the discussions are about climate change. Our agents' stance was defined by two variables: the strength of conviction about the urgency of climate action and the degree of trust in existing institutions. We quantified shifts in agents' "beliefs" by monitoring, across multiple rounds of conversations, (1) inter-agent distances in this two-dimensional stance space and (2) the patterns of discussion topics as modeled by Latent Dirichlet Allocation (LDA). Our findings to date suggest that significant abrupt changes in climate-change stance do occur in this simple model. We report a number of methodological lessons from this study, notably, the need to prevent LLM biases from interfering with the conversational dynamics and, more generally, to maintain agent personality and episodic memories of interactions in the face of such biases. Resolving these issues may allow for using ABM-derived insights in designing real-life interventions vis-a-vis climate change and other important societal challenges.

Data-driven control of dynamical systems has attracted significant research interest. This paper establishes a theoretical foundation for data-driven control in infinite-dimensional spaces by extending the notions of persistency of excitation, data informativity, and Willems' fundamental lemma. These extensions enable their direct application to systems governed by partial differential equations and delay differential equations.

Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncertainty quantification (UQ) approaches behave when adapted to geometry-conditioned neural surrogates. We compare one closed-form and two sampling-based approaches-a Gaussian process (GP)-based method, concrete Monte Carlo (MC) dropout, and deep ensembles-and evaluate them on three large, industry-relevant CAE datasets for external aerodynamics and crash dynamics. We examine whether predicted uncertainties have credible magnitudes, identify locations with larger prediction errors, respond to unfamiliar inputs, and remain informative for derived engineering quantities. On the DrivAerStar dataset, where all three methods are compared, each generally assigns higher uncertainty to locations with larger prediction errors, and validation-based rescaling brings interval coverage close to nominal on a disjoint in-distribution test set. Results on AirFRANS and automotive crash also show useful error ranking and interval estimates, but the relative performance of the methods changes with the dataset and evaluation criterion. UQ methods and evaluation metrics should therefore be selected based on the intended downstream CAE decision.

In this paper, we introduce the Directional Total Variation-Regularized Implicit Neural Representation (DTV-INR), an advanced variational paradigm that synergistically integrates coordinate-driven implicit neural networks with an anisotropic, structure-tensor-informed total variation regularizer tailored for resolution-agnostic image super-resolution. Casting the continuous-to-discrete acquisition process into an ill-posed inverse problem framework, our formulation equips a SIREN-architected coordinate network with a dynamic Riemannian metric tensor field D(x). By leveraging its spectral decomposition, the proposed regularizer preferentially directs diffusion parallel to dominant structural contours while penalizing cross-edge dissipation, successfully circumventing the classical staircasing artifacts inherent to scalar total variation schemes. We rigorously prove the well-posedness of this formulation in H^1(Omega) by establishing the existence, uniqueness, and metric stability of the variational minimizer, and realize this via an alternating projected optimization algorithm that decouples network parameter tuning from adaptive tensor field updates. Comprehensive experiments conducted on clinical brain magnetic resonance imaging (MRI) and biomedical transmission electron microscopy confirm substantial quantitative and qualitative improvements, yielding PSNR enhancements reaching +5.05 dB over baseline unregularized INRs and +1.71-2.85 dB over isotropic TV-INR across continuous (non-integer) upsampling factors, alongside remarkable noise robustness up to sigma_eta = 0.10 and monotonic preconditioned convergence behavior.

LoRa is a physical layer technology with the ability to connect multiple devices in a wide area of coverage, with low power consumption and with interference robustness. In this Letter, we investigate the efficiency of LoRa to send multiple uplink streams, analyzing strategies of allocating the spreading factor for coverage or capacity enhancement.

Inductive types are ubiquitous building blocks in many programming and theorem proving languages. An inductive type is a closed set of constructors from which values of the type can be created. That set cannot be extended though once a type is defined. This limits extensibility, reuse, and modular separation of concerns when defining types and functions operating over their values. This limitation is manifested in the expression problem, where extending an expression language with new syntactic constructors without having to modify or re-compile existing ones is a challenge in almost all programming languages. This paper presents inductive type and function implementation composition algorithms based on meta-programming. In addition, a set of syntactic extensions to the Lean proof assistant implementing those algorithms are presented. This framework allows for modular reuse, composition, and extension of a subset of Lean type and function definitions. In addition, semantic subtyping relations between component and composite types are discussed both at the type theoretic and implementation levels. The framework is demonstrated on a case study, involving the composition of syntactic and semantic artifacts of three sublanguages into one language. The case study highlights both the features and limitations of the composition framework.

Controlling the spatial distribution of absorbed optical energy is central to nanoscale photothermal chemistry, plasmonics, and ultrafast materials control. Here, we show that a metallic AuPt superlattice concentrates electronic energy in Pt within a few hundred femtoseconds, regardless of the initial energy distribution between the two constituents. Ultrafast X-ray diffraction follows this energy redistribution through the amplitude of a coherent 570 GHz superlattice phonon driven by the stress imbalance at the AuPt interfaces. Despite the nearly homogeneous absorption at 400 nm, the observed lattice motion is identical to that produced by 800 nm excitation, which is absorbed predominantly in Pt. This dissipation driven localization of energy arises from the large electronic heat capacity of Pt and rapid electronic transport through the superlattice, providing a route to femtosecond control of nanoscale energy distributions.

Energy networks face a paradigm shift driven by renewable integration, uncertainty about required flexibility, distributed markets, and smart demand. Increasing asset interactions, cyber dependencies on communication and computation systems, and the deployment of AI agents demand a holistic, system-wide approach to understand the system's emergent behaviour. These transformations affect energy generation, demand adaptation, grid operations, and market dynamics, forming a complex engineered system of systems. We argue that a complex-systems perspective can help to understand this evolution. Drawing lessons from two highly successful large-scale engineered systems, the Internet and agile software engineering, we highlight how prioritising design for evolution over traditional design for functionality enables energy systems to adapt to net-zero dynamics and handle unforeseen uncertainties. We discuss how the notion of federated energy communities (FEC), which aims for an open energy system with distributed coordination, aligns with this perspective. In FECs, each EC produces, stores, and manages its own energy, enabling it to trade with peers, respect grid constraints, and reach fair agreements. Beyond regulatory issues, the main challenge is identifying constraints that can orchestrate EC operations at the scale and reliability standards required of power networks, without unnecessarily limiting the innovation needed for system evolution. We then conclude with tentative design principles for future decentralised, self-organised energy networks through the lens of design for evolution, and how to apply them to a bottom-up architecture of autonomous energy communities.

In the classical i.i.d. prophet-inequality problem, a single item is allocated to one of $n$ agents who arrive sequentially, with values drawn independently from a known distribution. When an agent arrives, their value is revealed, and the algorithm must immediately allocate the item or continue. The usual objective is utilitarian welfare: the expected value of the recipient. Guarantees for this objective extend to allocating $m$ indivisible items to sequentially arriving agents with i.i.d.\ additive values. Utilitarian welfare, however, ignores how expected utility is distributed across agents. Motivated by a rich literature in fair division, we instead evaluate an online rule by its generalized $p$-mean welfare, which includes utilitarian welfare at $p=1$, Nash welfare (the geometric mean of utilities) at $p=0$, and egalitarian welfare (the minimum utility) as $p\to-\infty$. When the number of items is large, we show that this many-item fair-division problem is captured exactly by a single-item prophet problem evaluated by the $p$-mean of agents' expected utilities. We characterize this single-item problem: every online rule is weakly Pareto dominated by a quantile-threshold rule, and an optimal egalitarian rule equalizes agents' expected utilities. We prove that for every $n$, the online optimum is at least $\Gamma\approx0.7059$ times the prophet's egalitarian welfare; by monotonicity of generalized means, the same guarantee holds for every $p\le1$. Further, for egalitarian welfare, the optimal ratio converges to $\Gamma$ as $n\to\infty$. Thus, asymptotically, optimizing egalitarian rather than utilitarian welfare costs only about four percentage points relative to the classical utilitarian ratio of $0.7451$. Finally, when $m=n$, the worst-case competitive ratio converges to zero as $n\to\infty$ for every $p\le0$, showing that the large-item assumption is necessary.