Papers

Hyperscale artificial intelligence (AI) data centers are emerging as a structurally new class of electricity demand. Unlike conventional loads, they materialize as spatially concentrated, transmission-level point loads with rapid deployment timelines and converter-dominated dynamics. Their integration is governed by two defining properties: forecast uncertainty in load realization and multi-scale temporal variation spanning sub-seconds to planning horizons. We develop a unified framework that links reliability and affordability to these dimensions through a four-quadrant structure: (reliability, affordability) $\times$ (uncertainty, variation), which integrates probabilistic resource adequacy, generation and transmission expansion, operational security, and market design. Measured traces from a public generative-AI workload dataset show strongly tonal GPU power spectra rather than smooth broadband behavior: harmonic combs at the training-step cadence, and a distinct sub-second periodicity in inference. Across these traces the dominant variance band shifts with workload type (seconds for training and offline inference; tens of seconds and longer for online inference). We report this as a characterization of the measured workloads rather than a universal signature, and take it to indicate that such loads warrant a spectral description rather than a peak-demand one. These signatures directly affect reserve requirements, ramping products, voltage stability, ride-through performance, and harmonic interactions in converter-rich grids. Taken together, the analytical framework and empirical results establish a system-level basis for assessing the reliability and cost implications of large AI data center integration across planning and operational horizons.

Under the conditional framework breaking the longstanding O(n log n) integer multiplication barrier (originating from OpenAI Preprint #109), the asymptotic time complexity exponent T(n) = O(n (log n)^{1-\kappa}) is governed by bounding the second moment E[X^2] < 1 of recursive branching processes over trilinear tensor carrier graphs. In this work, we present a constructive combinatorial optimization over the alternating carrier bipartite matching graphs of the Schönhage trilinear tensor decomposition at dimensions h=23 and h=25. Through an alternating augmenting path search, we uncover a non-trivial cluster-unlocking cascade that eliminates 185 carrier roles (95 roles in h=23 and 90 roles in h=25), reducing the global physical wire width by 377,890 wires from the reviewed baseline W = 177,284,805 down to W = 176,906,915. Evaluated over the exact 10^{-14} rational grid, this wire reduction certifies an improved second-moment coefficient AB = 5,164,059 / 125,000,000,000 and establishes the sharpened conditional exponent \kappa = 826,215,307 / 20,000,000,000,000 \approx 4.131076535 \times 10^{-5}, strictly surpassing the preceding record on this architecture (\kappa \approx 4.123864 \times 10^{-5}). All 47 polynomial constraints and 7 rational security margins are audited in exact Q-arithmetic with zero floating-point error, and the fundamental wire reduction identity is formally verified in the Lean 4 interactive theorem prover without unproven axioms.

Efficient and durable phosphors made from abundant elements underpin energy-saving solid-state lighting, near-infrared light sources for sensing, and X-ray and biomedical imaging. Co-doping is a standard route to brighter phosphors, yet the fate of the co-dopants is rarely established. We combine quantitative electron paramagnetic resonance (EPR) spin counting with photoluminescence, photoluminescence excitation, and X-ray-excited spectroscopy across two dilute Mn/Cr co-doping series of hydrothermally grown $\mathrm{ZnAl_2O_4}$ nanoparticles and show that the two ions can form an exchange-coupled, edge-sharing Cr–Mn defect complex, with $\mathrm{Mn^{2+/4+}}$ entering an octahedral site next to $\mathrm{Cr^{3+}}$. The octahedral Mn lifts the inversion symmetry of the $\mathrm{Cr^{3+}}$ site and strengthens its parity-forbidden absorption, enhancing the $\mathrm{Cr^{3+}}$ emission without energy transfer. The population of the defect complex follows the law of mass action, and above a threshold Mn concentration, Mn re-partitions into EPR-silent octahedral configurations that quench both emissions. Concentration optima in co-doped phosphors can thus reflect defect speciation, not only energy-transfer efficiency, which opens a structural design handle for brighter emitters.

Whole-slide images (WSIs) are gigapixel-scale digital scans of histopathology tissue and serve as the primary basis for cancer diagnosis. Existing histopathology generative models operate at the patch scale, producing fixed-size tiles of at most 1024$\times$1024 pixels which encompass only a small fraction of the WSI. In contrast, text reports for clinical diagnoses and slide-level diagnostic labels – the supervision that exists at scale – operate at the whole-slide level. We present BigCell, the first approach to generate coherent whole-slide histopathology images at native gigapixel resolution. BigCell trains a flow-matching transformer at 2048$\times$2048 pixels on over 120,000 publicly available WSIs spanning multiple organ types. Conditioning on embeddings from pathology foundation models and using an inference-time sliding-window pipeline, BigCell generates coherent images of up to 32,768$\times$32,768 pixels, outperforming prior tile generators on both tile-level and slide-level fidelity metrics. To make gigapixel synthesis practical, we introduce an adaptive scheduling strategy that prioritizes important slide regions, speeding up image generation by over 3\ttimes with minimal quality degradation. Furthermore, we propose the first text-to-image synthesis at 8k resolution by training a separate model that produces dense conditioning grids directly from pathology text reports. We demonstrate that augmenting with synthetic samples improves slide-level few-shot classification performance by up to $18 \%$ over baselines trained on real data.

Augmentation-based self-supervised learning can recover the content shared across views without separating its underlying factors into individual coordinates. We ask whether augmentations can be designed to make those factors identifiable. Our approach allows content factors to fluctuate across augmented views while preserving their mean for each source instance. Each instance receives a fixed, recorded set of augmentation strengths that controls how much its factors fluctuate. When factors respond differently to changes in these strengths, their patterns of variation provide information that distinguishes them. Under suitable decoder and support assumptions, we prove that these differences identify individual factors in a conditional Gaussian model, up to permutation, scaling, and translation. We then develop a learner that uses the recorded strengths to estimate these patterns jointly across instances, enabling learning from few views per instance. Synthetic experiments demonstrate near-perfect factor recovery through nonlinear mixing. Controlled dSprites experiments show improved coordinate alignment using augmentations that target known factors, even without telling the learner which augmentation corresponds to which representation coordinate. These results suggest a route to component identification in self-supervised learning: augmentation design can supply identifying information beyond shared content alone.

Quantum signal processing (QSP) requires the efficient computation of phase factors associated with a polynomial transformation. One existing stable factorization method avoids direct root finding but relies on Prony's method to recover a polynomial from weighted power sums of its roots (arXiv:2202.02671). We present a modification of this approach that eliminates Prony's method by using the logarithmic derivative of an associated polynomial. Because the logarithmic derivative has the same residue at every root after accounting for multiplicity, its Fourier coefficients directly yield the unweighted power sums of the roots inside the unit disk. The Newton–Girard identities then recover the coefficients of the corresponding polynomial without computing its roots. The resulting algorithm has $O(d\log^2 d)$ computational complexity and simplifies the factorization procedure of the original method. In numerical experiments on Hamiltonian simulation, eigenstate filtering, matrix inversion, and the Fermi–Dirac operator, our implementation computes phase factors in seconds with maximum errors on the order of $10^{-12}$.

Regularization-based continual learning protects each parameter in proportion to an estimate of its importance, yet these estimates come from finite samples and heuristics and are used as if they were exact. We report four studies that start from a biologically inspired mechanism and end with a statistical explanation of it. Motivated by dendritic nanotubes, we let transient lateral links diffuse importance tags between hidden units. Links between co-active units gave no significant gain, but random links with lifetimes of 25 or 200 steps raised final accuracy on 20-task Permuted MNIST by 1.5 to 2.6 points. We show that random diffusion implements linear shrinkage of importance toward the layer mean in expectation. A simulation of the link process alone predicts shrinkage weights of 0.23 and 0.52 for these lifetimes, and graph-free shrinkage at 0.25 and 0.5 reproduces both the accuracy and the dispersion of the consolidated importance, while every activity-dependent rule did worse than random links. A five-seed screen across EWC, SI, and MAS found nominal gains for SI and MAS on Permuted MNIST and losses on task-incremental Split CIFAR-100, where forgetting was small and shrinkage cost plasticity. Varying the number of importance samples then separates two mechanisms on Permuted MNIST. For EWC, the gain fell by about ten points per tenfold increase in samples, from 19.6 points with 10 samples to -0.4 with 1000, a variance effect. For MAS, a gain of about one point persisted at 1000 samples, consistent with a bias in the importance measure rather than noise. Shrinkage had no detectable effect for MAS on a domain-incremental CIFAR-100 benchmark. Finally, we show that a standard heteroscedastic empirical Bayes rule shrinks the largest Fisher-type estimates most, which may explain its poor results, and point to a log-scale alternative.

Let $\kappa_{\mathbb{K}}$ be the residue at $1$ of the Dedekind zeta function of a number field $\mathbb{K}$. We prove explicit upper and lower bounds for $\kappa_{\mathbb{K}}$ under the Generalized Riemann Hypothesis (GRH). Previous explicit bounds of comparable generality are weaker and require a weak form of Artin's holomorphy conjecture: our bounds improve the constants while assuming only GRH for the relevant Dedekind zeta functions. The new lower bound enables all imaginary quadratic fields with class number $\leq 2000$ to be detected (assuming GRH). Furthermore, we demonstrate that the upper bound can be significantly reduced when considering extensions of any fixed, nontrivial field.

Self-assembled monolayers (SAMs), formed by the adsorption of a monomolecular layer of adsorbate onto a surface, have emerged as leading candidates for plat- forms for electrochemical biosensors. In order to characterize the working age of a SAM-based biosensor, it is necessary to understand the long-term degradation of the monolayer, with particular emphasis on the intermolecular forces present in the self-assembly process. In this work, discrete- and continuous-time proba- bilistic cellular automaton (PCA) models for the degradation of SAMs involving adsorbate-adsorbate interactions are proposed in which adsorbate molecules desorb at a rate dependent only on the number of adsorbed neighbors. Impor- tantly, we make no assumptions on the relationship between degradation rate and adsorbed neighbors. Using techniques from generating function theory and complex analysis, the expected degradation curve is solved for explicitly in one dimension and shown to be a sigmoid curve related to the Gompertz function.

Deploying large language model (LLM) inference at scale requires jointly selecting hardware layout, parallelism strategy, scheduling policy, admission control, and request routing to meet latency and throughput targets. These choices interact: a routing decision that improves cache locality can concentrate load, and an admission threshold that triggers only at saturation allows queues to grow deep enough to degrade critical-tier traffic. Evaluating candidates on GPU clusters is too expensive for iterative exploration, yet existing predictive tools either ignore batching and queueing dynamics or model only fragments of the pipeline. In this paper, we present BLIS, a deterministic, CPU-only discrete-event simulator that models the full inference serving pipeline (admission, routing, scheduling, prefill/decode execution, KV-cache management, and preemption). BLIS pairs analytical basis functions with learned scaling coefficients and overhead terms, fit once globally, to predict step latency without per-model or per-GPU profiling. Across 36 experiments spanning six models and three GPU types, BLIS achieves 6.7% median end-to-end error while running around 200 times faster than real execution. In a configuration search over 420 serving configurations for Llama-2-70B, BLIS identifies a 4-GPU deployment that meets a 300ms mean TTFT service-level objective (SLO), whereas competing tools either require double the GPUs or recommend configurations that fail under load. Two policies evolved entirely in simulation were validated on real hardware and merged into llm-d, a widely adopted open-source platform for distributed LLM serving: an admission policy that reduces critical-tier TTFT P90 by up to 82%, and a flow-control policy that reduces E2E P50 latency by 32-48% on overloaded workloads.

Text-to-motion generation typically relies on dataset-specific skeletal representations, with models trained separately for benchmarks with different joint layouts. We investigate whether image diffusion architectures can model 3D human motion through a common image-compatible representation that accommodates heterogeneous skeletal layouts while preserving motion-specific kinematic structure. To this end, we organize root-centered joint trajectories into topology-informed joint–time images and model global root dynamics through a complementary latent stream. A motion autoencoder conditions local-motion decoding on the root latent, while a text-conditioned Scalable Interpolant Transformer (SiT) jointly generates both latent streams, with supervision on decoded 3D joint positions further constraining generation in motion space. In addition to dataset-specific models, we train a single motion autoencoder on HumanML3D and KIT-ML, followed by a single text-conditioned SiT shared across both datasets, preserving their respective skeletal definitions without skeleton retargeting to a common joint layout. Experiments on HumanML3D and KIT-ML show that our dataset-specific models achieve state-of-the-art performance, while shared training yields further gains on both benchmarks, demonstrating the benefits of shared modeling across heterogeneous skeletal layouts.

Slider-based control aims to give users continuous, fine-grained control over the intensity of individual edits in instruction-based image editing. However, existing approaches fail to deliver reliable continuous controllability: traversing a slider can produce abrupt visual jumps and non-monotonic changes, while jointly controlled sliders can interfere with one another. To systematically study these limitations, we introduce SlideBench, a comprehensive benchmark for continuous image editing spanning diverse editing categories and equipped with a unified suite of metrics quantifying monotonic progression, perceptual continuity, and inter-slider disentanglement. Building on these observations, we propose SliderEdit++, which explicitly regularizes the intermediate editing trajectory rather than supervising only its endpoints. Our method combines velocity- and semantic-space trajectory regularization with spectral control to encourage smooth, predictable slider traversal, together with a disentanglement objective that reduces interference between independently controlled edits. On SlideBench, SliderEdit++ achieves state-of-the-art performance, improving the overall score by 18.5% relative to the strongest baseline. At the same time, using a few-step editing backbone makes our method approximately 3x to 20x faster than existing slider-based approaches, enabling substantially more responsive interactive editing.

Looped transformers reuse the same layer multiple times, allowing inference compute to be adjusted without changing the model. Recent adaptive-depth methods train the model across multiple loop depths from the beginning of training. We introduce fixed-first training, which varies model depth only during a short final phase of training. At 200M parameters, training a model of fixed-depth 2 for the first 67% of the run reduces modeled training compute by 45% while keeping mean negative log-likelihood (NLL) across inference depths within 0.5% of training across depths throughout. At 1B parameters, training initially at depth 4 reduces modeled compute by 31% to 37% and wall-clock time by 32% to 39%, while keeping final NLL within 0.8% and downstream differences within the observed seed variation. These results show that training over the full range of depths can be reserved for a short finishing phase with only small changes in performance.

The second Jones problem (2011) consists in determining whether there exists a convergent positive series for which the ratio of consecutive terms has a limit and the set of subsums is a Cantorval; in the survey by Gł{\k a}b and Prus-Wiśniowski (2026) this problem is included in the list of open problems. In this paper, a family of such series is constructed explicitly as combinations of blocks of the form $\frac{2^k-1}{2^t} + \frac{2^{k-1}}{2^t} + \frac{2^{k-2}}{2^t} + \cdots + \frac{2}{2^t}$, where $t$ is the index of the last term of the block in the series and $k\ge2$ is the length of the block. For each series of the family it is proved that its set of subsums contains an interval and is not a finite union of closed intervals, and hence is a Cantorval. The proof relies on mixed-radix numerical systems with a redundant alphabet and uses an idea of Guthrie and Nymann (1988). If the lengths of the blocks tend to infinity, then the limit of the ratio of consecutive terms of such series is $\tfrac{1}{2}$, which, by a result of Jones, is the only possible value of the limit for which the set of subsums of a series can be a Cantorval. Thus, an affirmative answer to the second Jones problem is obtained.

We consider a multi-hop wireless network where energy-harvesting nodes rely solely on ambient radio-frequency interference as their power source. The goal is to deliver a packet from source to destination with minimum latency while guaranteeing a target end-to-end outage probability under Rayleigh fading. This gives rise to a joint routing and power allocation problem in which interference plays a dual role: it provides harvestable energy, but also impairs link reliability. We first transform the intricate, multiplicative end-to-end outage constraint into an additive form. Then, we propose two optimal algorithms. The first, HOPE, minimizes the bottleneck harvesting latency, i.e., the longest energy-accumulation time along the path, by reducing the problem to a least-cost path computation on a graph with interference-aware link weights. The second, THOPE, extends the objective to total end-to-end latency, adding the cumulative transmission delay, and likewise admits a closed-form least-cost path solution. Both algorithms are solved in polynomial time via Dijkstra's algorithm and yield explicit expressions for the optimal transmit powers. Extensive simulations reveal that HOPE and THOPE reduce the average total latency by up to an order of magnitude compared with shortest-path and minimum-energy benchmarks, while exhibiting sharply concentrated delay distributions that are largely insensitive to interferer density.

In his paper, ”Sur la distribution des fractions irréductibles de dénominateur $n$ ou de dénominateur au plus égal à $x$”, Hubert Delange considers the family integrals defined by \begin{equation*} \int_0^1\left(\frac{N(n,t)}{\phi(n)}-t\right)^{2q}dt, \end{equation*} where $n>1$ and $q>0$ are positive integers, $\phi$ is the Euler totient function, and for any real number $t>0$, $N(n,t)$ counts the number reduced fractions whith denominator $n$ that belong to the interval $]0,t]$. He was able to evaluate the integral for $q=1$ but stated that ”Malheureusement, nous n'avons pas su jusqu'à présent faire cette évaluation pour $q>1$”. In addition to its intrinsic interest, this calculation would help understand the asymptotic distribution of the $\phi(n)$ totatives of $n$ relative to $\phi(n)$ equidistributed numbers in $[0,n]$. In this paper, we first provide some general properties of the integral for any $q>1$ and reduce the problem to its calculation for odd square-free integers with at least two distinct prime factors. We then analyse into more detail the case $q=2$ for which we provide a formula that reduces the problem to the evaluation of the fourfold Möbius sum, of integer valued modular sums related to generalized Dedekind sums.

Diffusion models provide expressive trajectory priors for multi-robot motion planning (MRMP), but scaling them to large teams requires coordinating individual motions without expensive joint computation. We introduce Akule, a sparse interaction diffusion framework that augments a frozen single-robot prior with three learned modules: a reusable pairwise correction model $R_{\phi}$, a contextual selector $U_{\psi}$ that determines which corrections to evaluate, and a composer $G_{\omega}$ that combines their effects through context-dependent signed weights. This decomposition separates which interactions merit computation from how their effects should be combined into coordinated denoising updates. We train $R_{\phi}$ using matched pairwise trajectory optimizations, then learn $G_{\omega}$ and $U_{\psi}$ from physically optimized joint trajectories without requiring a prescribed ground-truth interaction graph. The resulting joint proposals are passed to a downstream search-based planner for validation and repair. Across diverse MRMP benchmarks, Akule achieves competitive planning success, complete-planner speedups of up to $25\times$, zero-shot population transfer, and successful planning with up to $256$ robots. Ablations further demonstrate that learned selection and composition reduce pre-repair conflicts and downstream repair effort relative to heuristic selection and uniform summation.

Magnetic actuation scales with a particle's magnetic moment, yet practical colloidal suspensions remain superparamagnetic or weakly magnetized, a permanent dipole drives a near contact attraction growing as the square of the moment, binding particles irreversibly. Here we show that this constraint depends not only on how much magnetic material a particle carries, but on where it sits. Partitioning a fixed moment M into N internal elements leaves the far field interaction, and every actuation force, unchanged while suppressing the near-field pair energy by 1/N. As we show in our experiments across 57 samples and three geometries, stability collapses onto a single $\sim M^{2}/N$ boundary, raising the accessible dipolar energy scale nearly 150-fold. A liquid-phase analogue of magnetic force microscopy images the engineered energy landscape directly. The resulting colloids outrun size-matched superparamagnetic beads in weak fields far from a magnetic source, suggesting their applicability in hard to reach places. Together, these results open a new operating regime for colloidal manipulation, with impactful implications in microfluidics and drug delivery.

Variance-based methods recover a Gaussian linear structural equation model (SEM) with equal or suitably constrained error variances, either by recursively identifying the source nodes with smallest conditional variance (top-down method) or sink nodes with highest conditional variance (bottom-up method). We show that the use of conditional variance is incidental: replacing it with the conditional risk, i.e., the minimal expected loss of linear prediction under the negative log-likelihood of the noise distribution, extends both methods to non-Gaussian noise. Existing methods are the least-squares special case. This yields two main results. First, exploiting the noise distribution improves structure recovery: the matched-loss procedures recover the SEM more accurately than their least-squares counterparts and the LiNGAM methods, which are designed for non-Gaussianity. Second, the two methods, interchangeable in the Gaussian setting, separate under non-Gaussian noise: the top-down method is correct for every noise density with finite differential entropy, whereas the bottom-up method requires a regularity condition and can fail without it, for instance under mean-zero exponential or Cauchy noise. Simulations confirm both results.

An LLM-directed excavator can execute mechanically feasible motion whose destination or authority no longer matches the operator's approval. We propose execution-bound authorization for the approval–dispatch–execution interval. A one-use lease binds the action, generated motion, mission contract and admission tolerance; atomic dispatch rechecks current authority and measured joint drift. Periodic supervision detects revocation and requests a quintic stop with a carry-pitch endpoint, selected through sampled joint, stroke, flow and reference-acceleration checks. The framework connects exact motion identity to dispatch integrity and load-aware interruption. Evaluation combines a 672-case interface suite, four loaded digging cases in synchronous simulation, unloaded MuJoCo/Pinocchio transfers and two command-level LLM planners. The gateway admitted all 120 benign interface cases and produced zero unauthorized dispatches in the attack suite. Loaded dispatch-window tests produced zero unauthorized deposition. During simulated dump-phase revocation, maximum closed-site deposition decreased from 1.23 to 0.33\,m$^3$; loaded-slew stops used less than 75% of nominal swing torque. These results demonstrate motion-bound authorization and quantify the retention and stopping behavior of supervised excavation skills.

We perform the first comprehensive experimental characterization of power consumed by real HBM2 DRAM chips. Our extensive characterization yields 1) the empirical basis for developing new, accurate HBM power models or validating existing power models and 2) key insights into structural and data-pattern-dependent variation of power in HBM2 chips. Out of our 13 new findings and 6 key takeaway messages, we highlight: 1) a read operation consumes significantly higher current than any other operation and 2) the toggled data bus signals in a data transfer burst significantly affect current draw where toggling all HBM2-internal bank group bus signals causes 29.4% higher power consumption than keeping them constant. Leveraging our empirical insights into HBM2 power consumption, we engineer an access pattern that yields 23.6% higher power consumption on average across 36 tested HBM2 chips than the highest-power-consuming JEDEC-specified current measurement loop. Our results have important implications for HBM-based system design and validation. Relying solely on JEDEC- or vendor-specified test loops to bound HBM power could cause system failures and/or thermal throttling in real-world high-power AI/ML workloads. To improve 3D-stacked DRAM power modeling in open source architectural simulation infrastructures, we develop a new HBM power model. Our model predicts the power of 36 real HBM2 chips across diverse workloads (including a real LLM decode workload) with 7.6 – 8.1% mean absolute percentage error, substantially more accurately than state-of-the-art HBM power models. The power consumption predicted by our model for a power-intensive microbenchmark closely matches (with 2.4% to 5.3% error across HBM3E's specified supply voltage range) the average HBM3E memory power consumed by three tested NVIDIA H200 GPUs. We publicly release our power model at https://github.com/CMU-SAFARI/HBM-Power.

We determine the dynamical degrees of bimeromorphic automorphisms of hyperkähler manifolds of all known deformation types with irreducible characteristic polynomial.

We investigate the perturbative renormalization of Noether currents associated with chiral symmetry and supersymmetry transformations in $\mathcal{N}=1$ supersymmetric Yang-Mills theory, regularized on the lattice using improved discretizations. In particular, we study the chiral current and the supercurrent operator for a broad class of lattice actions: Wilson fermions with one-step stout-smeared links and a clover term, together with a family of Symanzik-improved gluon actions. Since the supercurrent mixes with both gauge-invariant and gauge-noninvariant operators, we compute the corresponding renormalization factors and mixing coefficients at one-loop order. We analyze the impact of improved gluon and gluino actions on this mixing pattern and investigate whether suitable choices of lattice parameters, such as the clover and stout coefficients, can reduce unwanted lattice artifacts at one loop. Our results provide perturbative input for the implementation of Ward identities and for matching lattice observables to their continuum counterparts, while also offering guidance for simulations aimed at restoring supersymmetry in the continuum limit.

By the Strong Perfect Graph Theorem, every graph whose chromatic number exceeds its clique number contains an odd hole or an odd antihole. We investigate the structure of odd antiholes in critical graphs with fixed maximum degree. We prove that if $G$ is a $k$-critical graph with maximum degree $\Delta$ then every odd antihole in $G$ has length at most $2(\Delta-k)+7$, and conjecture that, in the odd-hole-free setting, equality forces the graph itself to be the corresponding odd antihole. We verify this extremal characterization when $\Delta\geq 2k-5$, extending recent results for $\Delta=k$, and construct $k$-critical odd-hole-free graphs showing that the next possible odd antihole length $2(\Delta-k)+5$ below the extremal bound can occur. Our proofs use a list-coloring theorem for graphs on $2\ell-1$ vertices whose complements are hypomatchable. This motivates the conjecture that every odd antihole $\overline{C_{2\ell-1}}$ is strongly $\ell$-chromatic-choosable; we show that this conjecture would imply the full extremal characterization. We also obtain degree and attachment restrictions for odd antiholes in critical graphs.

This article presents an introductory study of $p$-differential forms in spinor variables defined on the Minkowskian (or Lorentzian) manifold. Starting from the algebraic and geometric foundations of spinor spaces and Clifford algebras, we establish the correspondence between Minkowski spacetime and Hermitian matrices in spinor coordinates. Within this framework, we construct differential 1-forms and 2-forms expressed in spinor notation, and formulate the Dirac operator in terms of exterior calculus. Furthermore, we extend this approach to the case of non-monogenic functions, following the method proposed in~\cite{Jaramillo2024}. The results illustrate the consistency of the spinorial exterior calculus and its potential applications in the study of relativistic field equations and geometric formulations of quantum theory.

We propose a rational comparison between several well-known machine-learning interatomic potentials (linear atomic cluster expansion, the Behler-Parrinello high-dimensional neural network potential, and the graph neural network-based MACE potential) by testing their performance for fitting classical potentials such as the Lennard-Jones and Stillinger-Weber potential. With this we assess their advantages and limitations regarding several aspects: varying training dataset size, robustness to noise, carbon footprint, as well as the ability to reproduce the radial distribution function as an example observable. Overall the MACE models are shown to most accurately reproduce the potential energy surface, with little sign of overfitting, but at a significant computational cost, highlighting important questions regarding the choice of models in computational materials science.

LLM data engineering requires iterative experimentation to determine how data selection, rewards, and curricula affect model learning, making it a natural setting for AI-for-AI (AI4AI) research. Can agents use experimental feedback to progressively improve strategies, and do the resulting strategies improve target-model performance on held-out data? We study how agents use experimental feedback to develop data-engineering strategies under fixed training and evaluation protocols. Our Agentic Data Engineering (ADE) framework lets agents pursue, revise, or combine research directions using cumulative findings. Strategies are selected by in-loop scores and evaluated on held-out benchmarks. Across four tasks-math and code data selection, math reward design, and math curriculum learning-selected strategies achieve absolute gains over generic baselines of up to 13.34% on AIME25 Pass@32 and 5.85% averaged across four held-out benchmarks under fixed training conditions. In-loop scores improve over successive experiments, while held-out trajectories show that later in-loop gains do not always improve generalization. Comparisons of research organization and feedback access favor combining evidence analysis with cumulative findings. Research trajectories show how earlier findings inform strategy revisions and combinations across research directions.

Physically connected humanoids need consistent dynamics for internal actuator loops, inter-robot forces, and changing ground supports. We extend RoboCompiler with member-wise dynamics assembly, compiling reduced dynamics from rigid bodies, moving actuator parts, and reflected rotor inertias. Compiled body Jacobians and analytic constraint curvature yield an explicit Coriolis factor satisfying the power identity for floating-base quasi-velocities. A two-level reduction retains reusable robot models while composing their supports and hand connections; local inertial updates have rank at most six, and prescribed-acceleration constraint wrenches are affine in actuator efforts. These interfaces support actuator-aware tracking, coupled force allocation, payload updates, and support-mode switching for five hand-linked humanoids. Across 264 feasible states in eight humanoid configurations, normalised acceleration discrepancies remain within $1.6\!\times\!10^{-10}$ against a hard-constraint reference and $1.4\!\times\!10^{-10}$ against a compiler-independent reference; MuJoCo simulations achieve 0.73~mm root-mean-square (RMS) pelvis error in the ring dance and complete side steps through 20 support-mode changes.

A classical uniformization theorem of Ahlfors from 1963 asserts that every bounded turning planar arc is the image of the unit segment under a quasiconformal self-map of the plane. We prove an analogous uniformization theorem for planar trees by showing that every planar quasiconformal tree with uniform branch separation is quasiconformally equivalent to a quasiconvex planar tree with uniform branch separation and Hausdorff dimension arbitrarily close to 1. Along the way, we show that every quasisymmetric (resp. bi-Lipschitz) homeomorphism between planar quasiconformal trees that respects the counterclockwise orientation of the branches at every branch point can be extended quasisymmetrically (resp. bi-Lipschitz) to the whole plane. As a corollary of the extension theorem we construct a large class of quadrivalent quasiconformal trees, which includes the Vicsek fractal, so that each tree in this class is the Julia set of a uniformly quasiregular map of $\mathbb{R}^2$.

Information of the tire-road friction coefficient is critical for intelligent vehicle systems, as friction establishes the limits at which the vehicle can be manoeuvred without loss of control. While there is extensive literature on online friction estimation, no previous studies have explored post-processing and mapping friction coefficients along a driven trajectory based on recorded sensor data. Mapped friction information could be shared by connected vehicles, enabling proactive measures in low-friction areas. This paper presents an offline post-processing method, FrictionMap, for mapping friction coefficients from recorded driving data. The method operates on commonly available on-board vehicle sensor information, and requires only a basic vehicle parameter set and a slip threshold as prior knowledge. FrictionMap runs an extended Kalman filter combined with a Rauch-Tung-Striebel smoother to estimate vehicle dynamics. Data points where the friction limit is observable are identified by filtering points based on tire slip. A Gaussian process is fitted to these points to acquire a continuous estimate of the friction coefficient along the trajectory. FrictionMap is validated via a simulation study, and shown to outperform commonly used online friction estimation techniques. The code implementation and the simulation benchmark are released as open-source after paper acceptance to enable further research.