Papers

Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI 2024) reveal a preference for dynamical dark energy with an equation of state parameter crossing the phantom divide ($w < -1$) at low redshifts. We investigate whether this phantom crossing can be realized within scale-invariant scalar-tensor theories featuring non-minimal derivative coupling (NMDC) between the scalar field and the Einstein tensor. Employing the effective field theory of dark energy formalism, we systematically derive the ghost-free and gradient stability conditions, and examine their compatibility with the swampland conjectures from quantum gravity. We establish three rigorous no-go theorems demonstrating that: (i)~phantom crossing necessitates $\xi_{\text{eff}} < 0$, directly violating the no-ghost stability requirement $\xi_{\text{eff}} > 0$; (ii)~the swampland de Sitter and distance conjectures independently obstruct phantom crossing; and (iii)~these theoretical obstructions are mutually reinforcing. Our results show that scale-invariant NMDC models cannot account for the DESI preference for $w < -1$, providing robust theoretical guidance for dark energy model building beyond this class.

Despite the growing number of gravitational-wave (GW) detections, the formation of merging binary black holes (BBHs) is still debated. One of the proposed formation channels is Chemically Homogeneous Evolution (CHE), which makes distinct predictions for the properties of the resulting black holes (BHs): high masses ($\gtrsim35\, M_\odot$) and large, orbitally-aligned spins. These predictions are based on studies that consider this channel only in isolated binaries. However, most massive stars reside in triples. We investigate how a tertiary affects the CHE channel. We use detailed binary models computed with MESA for the inner CHE systems coupled with analytical prescriptions for the hierarchical triple dynamics. Specifically, we study the von Zeipel-Lidov-Kozai mechanism that can accelerate the merger of the inner BBHs through high-eccentricity excitations. We show that a tertiary companion enables mergers at higher metallicities, where the classical binary CHE channel does not operate. At $Z_\odot/3$, triples produce BHs with lower masses (around $15\,M_\odot$) and lower spins (around 0.25) compared to the low-metallicity classical scenario. We further expect triple dynamics to lead to spin-orbit misalignment and potential residual eccentricities at merger. In triples at $Z_\odot/3$, half of the mergers occur within 1 Gyr. Moreover, 10% of the population leads to prompt mergers within 1 Myr (1% within 1 kyr) that are of potential interest for electromagnetic counterparts. We conclude that the triple CHE channel is promising as (i) it may contribute more substantially to the local merger rate than had been expected for the classical CHE channel due to the shorter delay times and effectiveness at higher metallicities and (ii) produces mergers with properties that more closely resemble the lower masses and lower spins inferred for most of the observed GW merger population.

Signal Temporal Logic (STL) inference provides interpretable formulas for time series classification. For multiclass classification, however, accurate predictions do not necessarily ensure that the inferred formulas are satisfied consistently with the true class. We introduce the positive satisfaction rate and codeword satisfaction rate to quantify satisfaction of required formulas and consistency with the complete class codeword, respectively. We develop a two-stage procedure that first learns discriminative formulas using a margin-based objective and then refines predicate thresholds toward a small positive robustness target while fixing the formula structure and temporal intervals. Satisfaction and ranking penalties discourage violations of required formulas and loss of class separation. The decoding loss is used as a nonconformity score and calibrated separately for each class, providing finite-sample class-conditional coverage under intra-class exchangeability. Experiments on naval, synthetic, and robot manipulation trajectories demonstrate discrepancies between classification accuracy and formula satisfaction. The results further reveal a data-dependent tradeoff between robustness tightness and satisfaction, while class-conditional calibration mitigates undercoverage that can be hidden by pooled calibration.

World-action models inherit broad visual and physical priors from video pre-training. However, standard within-video next-frame prediction allows them to rely on appearance shared between the context and future, rather than learning interactions that transfer across scenes and embodiments. We introduce WATCH, a cross-video pre-training that learns from task-paired human demonstrations collected across diverse environments. Conditioned on the video and actions of one demonstration, the model jointly predicts another demonstration's actions and future frames from its current observation. Predicting one demonstration from another encourages the model to learn task-relevant interactions that transfer across scenes and demonstrators. Our pre-training shows that these capabilities can be learned from readily scalable human-human pairs alone, without requiring matched human-robot demonstrations. Analyses before robot post-training show improved motion alignment across embodiments and better action and video prediction on unseen robots, with representations closer to those learned from robot pairs. After robot post-training, WATCH improves MimicDroid in-context success from 40.9% to 68.3% with Cosmos Policy and from 59.8% to 77.7% with Cosmos3, with the largest gains on the unseen levels. Gains persist under context-free post-training across robot embodiments. WATCH outperforms within-video pre-training and co-training baselines, supporting cross-video prediction as a scalable approach to learning transferable world-action representations.

Having demonstrated a strong potential for automating vulnerability discovery, AI agents can also be used to attack software systems at scale. Today's software systems need mechanisms to level the playing field by slowing down potential attacks, giving them time to patch vulnerabilities and strengthen software. Along this line, our study of agent trajectories in vulnerability analysis shows a surprising finding: agents produce dramatically different results across real-world code commits that carry the same functionality and the same vulnerability. This phenomenon appears consistently in multiple code domains and vulnerability categories. It motivates us to study natural and functionality-preserving code transformations derived from real-world software development, and their potential as a defense against attacker agents. We build a corpus of natural transformations by mining recurring development patterns from real-world code commits, and apply them to evaluate impact on agentic vulnerability analysis. Our results show that even a single form of transformation can effectively "confuse" frontier agents, e.g., Codex with GPT-6 Sol, reducing successes in vulnerability discovery. We also study different agent failures, whether transformations can be composed to provide stronger protection, and adaptive attackers who seek to reverse them. Overall, our study of natural code transformation significantly expands the research space of using code transformations to defend against malicious agents.

We show that continuous bitstream diffusion (CoBit), originally developed for language modeling, provides a unified framework for joint and conditional multimodal generation using the same training and sampling protocol. Across image-text, speech-text and protein sequence-structure modeling, models are trained separately from scratch, but each uses a single input projection, transformer backbone, bitwise prediction head and binary score-matching objective shared across its modalities. Within each setting, a single checkpoint supports joint generation and the conditional directions included in training by changing which parts of the bitstream are observed. We first validate the approach on MNIST-Sum, a controlled image-text task pairing raw binary images with equations encoded as text, achieving near-perfect conditional accuracy and high joint consistency without learned tokenizers. We then apply the same protocol at larger scale to speech-text and protein sequence-structure modeling. Trained without text pretraining, a single speech-text model performs speech synthesis, recognition, continuation, and unconditional co-generation. Jointly generated speech and text achieve 3.5% word error rate between the generated text and automatic transcriptions of the generated speech. In protein modeling, a single CoBit checkpoint supports forward folding, inverse folding, and joint sequence-structure generation. For jointly generated proteins spanning 100-500 residues, computational refolding of CoBit's sequences yields structures that agree with the generated backbones at a mean self-consistency TM-score of 0.911. Together, these results show that CoBit provides a common generative framework for substantially different modalities and forms of cross-modal dependence, without introducing a domain-specific objective or sampling procedure.

WR 6 is the prototype for periodic variability due to large-scale wind structures in Wolf-Rayet (WR) stars, showing a consistent periodicity of 3.76 d in photometry, spectroscopy, and polarimetry. However, the origin of this variability is debated, attributed either to corotating interaction regions (CIRs) or a low-mass companion. We use time-resolved interferometry to investigate the origin of periodic variability in WR 6. We aim to detect and characterize structures in the stellar winds of WR 6 and discriminate between the CIR and low-mass companion scenarios. Using the extended configuration of the Auxiliary Telescopes at VLTI, we obtained six GRAVITY epochs over six months to search for the presence and variability of wind-structures in WR 6. We also obtained complementary spectroscopic observations during one of the epochs to monitor contemporaneous spectral line variability. For all six epochs of GRAVITY observations: (i) WR 6 is consistent with a single star and has no spatially resolved companion detected above $M\gtrsim6\,M_\odot$; (ii) The He I line-emitting region is spatially resolved, while the He II lines remain unresolved, consistent with atmosphere models; (iii) Around 2.19 $\mu$m, discrete line-emitting features offset from the center of the star are detected. The number, positions, and wavelengths of these features vary across epochs. Spectroscopic monitoring reveals spectral line residuals that broadly correspond to the two features seen in the GRAVITY data of the fifth epoch. Finally, the first three epochs, observed on three consecutive nights, show significant variability in these features but cannot be directly linked across epochs. We thus report the detection of multiple large-scale structures in the wind of WR 6 with VLTI/GRAVITY. We favor CIRs as their likely origin owing to temporal and spatial variability that cannot be reconciled with a low-mass companion.

Quantile regression has received considerable attention in high dimensional methodology due to its robustness and ability to accommodate heteroskedasticity. Despite this attention, current inferential methods for high dimensional quantile regression have significant limitations—only testing significance, testing at a single quantile at a time, or assuming homoskedasticity. To generalize the inferences that can be drawn in high dimensional quantile regression, we introduce partial penalized Wald and rank score tests for testing linear hypotheses uniformly over a set of quantiles $\mathcal T$ under a heteroskedastic model. We propose globally adaptive local linear approximation (LLA) algorithms for folded concave penalized estimation and show that our global LLA algorithms recover “testing oracles” for the full and reduced models with high probability. We then show that our global LLA estimators achieve the $\sqrt{s/n}$ oracle estimation rate uniformly over $\mathcal T$, establish Bahadur representations, and derive asymptotic distributions for the test statistics under the null and local alternatives. We develop a dual formulation incorporating adaptive penalty weights for the rank scores and use the strong oracle property to establish their oracle equivalence. Using empirical process techniques, we derive reference distributions based on suprema of squared Bessel processes, extending partial penalized inference beyond pointwise chi-square calibration.

Enterprise customer-support agents increasingly rely on Large Language Models (LLMs) to execute bounded, tool-using workflows. We study this problem through the lens of Skill LLMs: specialized executors that operate within a selected skill context and must complete a narrow, stateful workflow under policy and tool constraints. We present a benchmark construction pipeline that mines recurrent workflows from real-world transcripts, converts them into structured skill descriptions, maps them to tool requirements, simulates environment state with Model Context Protocol (MCP)-compatible mocks, and generates multi-turn tool-using dialogues. Using this benchmark, we conduct a large-scale zero-shot evaluation of 17 language models spanning closed model families and deployment-oriented open-weight models from 1.7B to 14B parameters, each judged independently by five strong LLM judges, plus a deterministic rule-based evaluator that checks tool coverage, hallucinated tool use, and unsupported claims. We find a consistent ranking in which GPT-5.4 leads by a wide margin and QWEN3.5-9B is the strongest open-weight model (below 20B), outperforming several closed baselines under every judge. We also find that judge choice is not a negligible methodological detail: pairwise judge agreement on the pass/fail verdict averages Kappa=0.524 across 10 judge pairs. These results suggest that comprehensive zero-shot evaluation of skill execution requires judge reliability as carefully as model capability.

We develop a framework for computing the nonlocal one-loop effective action in scalar and spinor QED at finite temperature and chemical potential in arbitrary even spacetime dimensions. Based on the heat kernel expansion to quadratic order in background fields, the framework reduces the effective action form factors to a common fundamental kernel. By resumming the external-momentum expansion, we obtain explicit closed-form expressions for the massless form factors in terms of polylogarithms and their derivatives with respect to the order. The same method determines the coefficients of the small-mass expansion to arbitrary order. The resulting expressions retain the full dependence on external Euclidean momentum, temperature, and chemical potential, without invoking the soft-momentum approximation. We also derive the corresponding photon polarization operators and evaluate their static limits, obtaining the Debye screening masses and electromagnetic susceptibilities.

Scaling deep learning models efficiently requires predictable performance transfer across compute regimes. Establishing reliable hyperparameter transfer allows optimal training dynamics and structural choices to be discovered on low-cost proxy models, avoiding catastrophic failures during massive-scale training. Existing depth-transfer analyses are architecture-specific and heuristic: hyperparameter transfer is only justified through toy blocks, and both rely on infinite-depth dynamics, a specific initialization, and feature-learning criteria. Building on $L$-smoothness framework of Xu et al. (2026), we understand hyperparameter transfer as how do the Lipschitz and $L$-smoothness constants of the loss scale with the depth $K$? We show that inverse-depth residual branch scaling $\alpha=\Theta(1/K)$ is sufficient to make both constants depth-independent at fixed width, uniformly over the bounded parameter domain and for arbitrary $p\to q$ geometries. Because the bounds depend on each residual branch only through its Lipschitz and smoothness constants, the argument applies to general residual networks (including branches of block depth $\geq 2$ such as transformer and ResNet blocks) without assumptions on initialization or correlations between layer weights. Since the smoothness constant controls the curvature penalty in the descent inequality, our bounds motivate a learning-rate scale without an additional depth-dependent curvature correction for updates bounded in the prescribed norm. This provides a geometric explanation of inverse-depth residual scaling and its application to the operator-norm geometries associated with AdamW, Muon, and MOGA. Learning-rate sweeps on GPT-2 (depths 2–128) and CIFAR-100 ResNets (8–32 residual blocks) confirm that Muon and MOGA exhibit stable learning-rate transfer under these prescriptions, with a common optimal rate across a 64-fold increase in depth.

We prove that Choe's higher-dimensional Enneper hypersurfaces in $\mathbb R^{n+1}$, $3\le n\le6$, cannot be confined between two parallel hyperplanes, disproving his slab confinement conjecture. We further strengthen this conclusion by determining their precise height growth exponent. If $H(R)$ denotes the maximal absolute height above the asymptotic hyperplane within the horizontal ball of radius $R$, then $H(R)=R^{\alpha_1+o(1)}$ as $R\to\infty$, where $\alpha_1=\frac{\sqrt{(n-2)^2+4\lambda_1(\Omega)}-(n-2)}{2}$, $\Omega=S^{n-1}\setminus[0,\infty)^n$, and $\lambda_1(\Omega)$ is the first Dirichlet eigenvalue of the spherical Laplacian. In particular, $0<\alpha_1<1$, so the height is unbounded but grows sublinearly. The proof combines the blow-down behavior of a fundamental piece of Choe's hypersurface with the rigidity of positive harmonic functions on cones. In dimension two, the formula gives $2/3$, recovering the classical Enneper height-growth exponent.

We present ContinuousCloth, a continuous-time, physics-informed neural solver for deformable cloth dynamics that enforces a spring–mass ODE within a neural trajectory model. Unlike classical time-stepping simulators that return trajectories only on a discrete integration grid, ContinuousCloth supports querying at arbitrary timestamps and computing displacement, velocity, and acceleration via automatic differentiation. We evaluate ContinuousCloth along two dimensions. In a physics-only setting, ContinuousCloth achieves trajectory accuracy comparable to high-precision solvers across six diverse boundary-condition scenarios while reducing runtime by up to 17.4 times. When fused with sparse and noisy observations, the spring–mass ODE acts as a strong inductive bias for downstream tasks: interpolation and parameter estimation. That is, ContinuousCloth reduces interpolation error by 7.3 times over a data-only neural baseline in simulation and 2.4 times on real-world cloth sequences, and achieves 2.6 times lower parameter error than a differentiable-solver baseline under high-noise conditions, demonstrating consistent robustness under realistic measurement imperfections.

We present CoPlanVLM, which uses a Vision Language Model (VLM) to translate a single natural-language instruction and image into coordinated paths for a team of two robots. While VLMs offer a flexible, natural-language interface for commanding robot teams, their weak spatial reasoning has greatly limited VLM-based path planning. CoPlanVLM improves the VLM's spatial reasoning and path planning abilities through three components: (1) an image overlay marking both free space and obstacles, (2) task classification that selects the most appropriate low-level planner and reasoning prompt for each instruction, and (3) task-specific chain-of-thought reasoning that prompts the VLM to identify key objects, allocate roles, and verify routes are collision-free before committing to a plan. Together, these components enable the team to complete complex coordinated maneuvers requiring both robots and divide large tasks between robots to increase efficiency. CoPlanVLM also supports detailed maneuvers involving specific routes, loops, and coverage of large areas, as well as tasks requiring directional reasoning such as north/south or left/right. We validate CoPlanVLM in both Gazebo simulation and on physical Turtlebot 4 hardware. CoPlanVLM attains an average success rate of 84.4% compared to 50.0% for the closest baseline. On trials where both methods succeed, CoPlanVLM's paths are 27% shorter on average. Project code is available at https://github.com/AICPS/CoPlanVLM.

We define a class of flows on compact metric spaces that we call \emph{$C^\alpha$ metric Anosov flows}, $0 < \alpha < 1$ or $\alpha = \mathrm{Lip}$. We give verifiable criteria for a metric Anosov flow to be $C^\alpha$. We show that $C^\alpha$ metric Anosov flows have Hölder continuous local product structure, and in particular Hölder continuous holonomies. We deduce that topological conjugacies between $C^\alpha$ metric Anosov flows are automatically Hölder continuous. We show that any $C^\alpha$ metric Anosov flow admits a strong (i.e. Hölder continuous) Markov coding. This yields strong ergodic properties for equilibrium states for Hölder potentials for $C^\alpha$ metric Anosov flows. The regularity of the local product structure is proved in a non-compact setting which applies for the geodesic flow on the universal cover of a locally CAT(-1) space. This allows us to obtain Hölder regularity results for the holonomy maps for pinched negative curvature manifolds with respect to the Sasaki metric. This contrasts with the result of Ballmann, Brin and Burns that there are examples in this class for which the dynamical distributions are not Hölder.

We propose an integrated market equilibrium model for determining the spot market prices and flow rates in a natural gas pipeline network. The traditional approach solves the market equilibrium model separately from the natural gas network flow allocation problem in a sequential manner. Our proposed framework synthesizes marketing and operations by using a bilevel optimization formulation where the market equilibrium model in the upper level is connected and simultaneously solved with the natural gas network flow model in the lower level. We introduce convex relaxations for the nonconvex Weymouth pipe pressure drop equation and a surrogate for the compressor operating cost. Furthermore, we compare multiple single level reformulations of the bilevel problem based on Karush-Kuhn-Tucker (KKT) optimality conditions, Wolfe duality, and Lagrange duality conditions. Numerical studies on a small 6-node network demonstrates the efficacy and accuracy of our model and the comparison between different duality and optimality based reformulations.

TREGO, a trust-region Bayesian optimization (BO) method for expensive blackbox problems, has convergence guarantees, but only for exact function values. In high dimension, its performance tends to deteriorate. This paper asks whether a trust-region BO method can be extended to handle noisy evaluations while being competitive in high dimension. We first generalize TREGO into a trust-region framework for noisy BO and extend its convergence analysis to noisy function estimates that are sufficiently accurate with sufficiently high probability. We then propose STREGO, a scalable implementation of this framework. Its global phase selects a batch of candidates by solving a bi-objective problem on the posterior mean of a Gaussian process and the integrated variance reduction. Unlike the predictive variance, this second objective does not favor boundary points merely because they are far from the data. Its local phase minimizes the posterior mean of a second Gaussian process, trained only on points close to the incumbent. STREGO is compared with TREGO, TURBO, BAXUS and NSMA-BO on synthetic and real-world problems of dimension $4$ to $124$, with and without noise. It gives the best average results in every synthetic setting tested and the best or tied-best solution on four of the six real-world problems. An implementation of STREGO is available at https://github.com/Mayousk/STREGO.

We establish variance upper bounds for the minimum perfect matching problem in general metric spaces under a geometric partition condition. As a principal application, let $H_n$ be the minimum perfect matching cost of $n$ independent uniform points in $[0,1]^d$, where $n$ is even and $d\ge2$. We prove $$\operatorname{Var}(H_n)\le C d n^{1-2/d},$$ where $C$ is independent of $n$ and $d$. This removes the logarithmic losses in earlier upper bounds in every dimension (Talagrand, 1995); in particular, the variance remains bounded in dimension two, answering an open question (Rhee, 1994). The proof relies on constructing a rapidly mixing Markov process with a multinomial stationary distribution.

Direct-to-device (DTD) satellites carry mobile base stations transmitting in terrestrial mobile bands. Their non-linear emission products can fall into radio astronomy bands, including passive bands. We measure the harmonics of the Starlink DTD downlink at 2620-2630 MHz and the intermodulation products around them, search for products next to the carriers, and compare them with the ITU-R unwanted-emission limits and radio astronomy protection criteria. We use autocorrelations of single Australia Telescope Compact Array antennas on tracked passes of DTD and other satellites with the 16 cm and 4 cm receivers. Harmonic ratios and receiver tests show that the harmonics are satellite-generated. We simulate the aggregate equivalent power flux density of a constellation at Effelsberg and the ATCA. The harmonics H2 to H4 at 5240, 7860 and 10480 MHz fall by about 16 dB per order, show no trend with elevation, and originate on the satellite. H2 is also detected in 32% of integrations more than 10 degrees from any DTD satellite. Inside the harmonic zones the spectra follow the n-fold convolution of the carriers; outside them, intermodulation products of order n+2 and higher lie on average 19 dB below the zone and switch between -23 and -15 dB within seconds. Next to the carriers no satellite emission is detected to 33 dB below the carriers. H2, >=-38.9 dBW in 4 kHz isotropic-equivalent, is at or above the SM.329 space-station limit; H3 and H4 meet it. For 8640 satellites the aggregate exceeds the protection criteria by 65 and 25 dB at the second and fifth harmonics, and by >100 dB for out-of-band emission at the mask level in 2690-2700 MHz. Harmonics are received far outside the serving beams. Their radiated level must be limited directly, not through the power at the antenna port. Compliance with per-satellite ITU-R limits does not protect radio astronomy from the aggregate of a constellation.

Latent world-model planning has shown promising results in goal-conditioned robotic manipulation, but remains challenging for long-horizon planning due to limited temporal guidance and inefficient action search. A distant visual goal provides little guidance for preparatory actions, while uninformed action sampling makes local optimization inefficient. We propose PILOT (Policy-Initialized Local Optimization with Temporal subgoals), which uses a video model to generate intermediate visual subgoals and a learned policy to initialize the cross-entropy method (CEM). CEM refines candidate action sequences toward each subgoal using an action-conditioned world model in a receding-horizon control loop. In our primary real-robot evaluation across four UR5e manipulation tasks, PILOT achieves 68.8% success, compared with 55.0% without policy initialization, 13.8% for policy-only execution, and 0.0% for direct final-goal planning. Simulation results show that these gains persist over longer horizons: PILOT exceeds direct execution of the same policy by 30 percentage points on long Push-T tasks and by 22 percentage points on LIBERO-10. Policy initialization also accelerates local optimization: on Push-T, CEM matches the cost reached by generic initialization after 10 iterations in only 4 iterations and reduces the final planning cost by 24.1% under the same sampling budget. These results show that combining temporal subgoals with policy-guided action search improves both long-horizon task execution and local planning efficiency. Videos are available on the webpage: https://pilot-planner.github.io/.

In Model Context Protocol (MCP) systems, LLMs select tools from metadata rather than from their implementations. Names and descriptions summarize what a tool does, while the parameter schema specifies the fields a tool accepts and how they are organized. Our analysis of metadata for 367,174 MCP tools reveals substantial schema variation among functionally similar tools. Many of these tools share names and similar descriptions but expose different parameter schemas. This raises a key question: can parameter-schema differences influence tool selection before any call is made? We study this question through controlled metadata interventions across five LLMs and five tasks. Each comparison changes exactly one metadata factor (server name, tool name, description, or parameter schema) while keeping the others fixed. We balance tool positions and use conditional logistic regression to estimate position-adjusted effects. We find that: (1) parameter-schema changes produce the largest and most consistent selection shifts among the tested interventions. Models tend to favor separate top-level parameters over grouped or composite forms. (2) Descriptions that explain parameters also tend to increase selection, while name effects are weaker and less consistent. (3) Targeted comparisons show that schema effects depend on the specific parameter names and on how the request represents the same information. When only one schema satisfies an explicit request requirement, all five models select the compatible tool despite position preferences. These results show that parameter schemas influence not only how tools are called, but also whether they are selected. For MCP developers and evaluators, schema design and tool ordering can therefore affect which implementation is invoked even when functionality is unchanged.

We study decentralized bandit learning in discounted infinite-horizon, general-sum Markov games with continuous actions. Agents observe the public state, but only their own realized rewards, and use simultaneous perturbation stochastic approximation to update their actions. Under strong monotonicity of the negative running-reward gradients and sufficiently small time steps, we prove that the fully decentralized procedure converges almost surely to the unique stationary Markov perfect equilibrium. We obtain an $O(n^{-1/2})$ convergence rate and present a natural extension to episodic finite-horizon learning.

Accurate sampling from continuous-time generative models can require many model evaluations. Low-step sampling reduces cost, but coarse updates introduce endpoint errors that can accumulate and degrade generation quality. We introduce TraceSampler, a post-training method that corrects these errors without modifying the pretrained model. Rather than optimising low-step updates directly, TraceSampler models endpoint error as a sample-specific prediction problem. A higher-step reference integration over the same interval provides the supervised target, while a compact representation makes high-dimensional error predictable from the sampling trace. This representation combines shared residual structure, trace-derived directions, and a low-rank remainder, so shallow per-step MLP heads predict sample-dependent coefficients. These coefficients drive a two-stage learned residual correction: the first stage predicts the full endpoint residual, while an intermediate backbone evaluation provides new trace information to predict the remaining residual; this evaluation is reused by the following step. TraceSampler is evaluated with Rectified Flow on CIFAR-10, SiT-XL/2 on ImageNet-256, and SD3.5 Medium for text-to-image generation. At 10 steps, it reduces trajectory MSE relative to matched-step Euler by 90.5% on CIFAR-10 and 85.6% on ImageNet-256, while achieving FID scores of 2.692 and 2.189, close to 120-step Heun references of 2.601 and 2.056 with 24$\times$ fewer backbone evaluations. On SD3.5 Medium, TraceSampler improves image quality and prompt following; at 10 steps, ImageReward rises from 0.752 to 0.906 while trajectory MSE falls by 70.7%. These gains preserve Euler's backbone-evaluation budget, add less than 0.4% inference FLOPs, and incur negligible wall-clock overhead, showing that coarse-step sampling error can be made predictable from the sampling trace and efficiently corrected.

The cardinalities of Kiselman's semigroups $K_n$ are known to grow double exponentially in $n$: the sequence $2^{-n/2}\log_2|K_n|$ converges along the even and odd $n$ subsequences to positive limits $c_{\mathrm{even}}$ and $c_{\mathrm{odd}}$ that appear to coincide. In this paper we prove that they are indeed distinct. Since Kiselman's semigroups are $\mathcal{L}$-trivial, the suffix relation defines a partial order on $K_n$. We introduce the Kiselman transform $\mathsf{Kis}(P)$ of a poset $P$, a construction recovering the poset associated with $K_{n+1}$ from that associated with $K_n$. Counting strictly increasing chains in $P$ and $\mathsf{Kis}(P)$ yields a linear recurrence governed by a symmetric infinite matrix with explicit binomial entries. This can be used towards efficiently computing $|K_n|$, allowing the values listed in OEIS sequence A125625 to be extended beyond $n=14$. A generating functions analysis gives formulas for the above asymptotic limits, together with rigorous numerical bounds establishing that \[ c_{\mathrm{even}} - c_{\mathrm{odd}} = 1.9945066605\ldots\times10^{-6} \]

Treatment decisions are often sequential and depend on information absent from the recorded history. Latent sequential ignorability models such assignment by assuming that baseline covariates and principal strata, defined by joint potential intermediate responses, account for confounding of later treatment. For two treatment periods with a binary intermediate response, we derive sharp population and principal effect bounds under a specified association between the potential responses and show that the two targets can require different optimizations to obtain sharp bounds. For population effects, optimization over latent treatment probabilities reduces to their feasible endpoints. Stronger selection between response types can be offset by making their outcome distributions more similar, preserving both the observed distribution and population marginal outcome distributions. This replacement can change effects within principal strata, whose sharp bounds may instead require interior treatment probabilities. Restrictions on differences in conditional effects can tighten the bounds without equating outcome levels. For binary outcomes, we give an exact finite algorithm that includes these interior assignments. We also develop inference under smoothness and estimation conditions. We illustrate the bounds in a study of gym attendance after an incentive program.

The Mallows model is a well-established construct in preference modeling, describing random rankings through their Kendall-Tau distance from a reference permutation. Its compact parameterization and interpretable treatment of preference uncertainty have made it influential across statistics, machine learning, probability, and revenue management. In the latter domain, recent literature has studied the embedding of Mallows-driven choice into assortment optimization. Early approximation schemes in this context require stylized structural simplifications or restrictive parametric assumptions. In the absence of these levers, a highly involved quasi-polynomial-time approximation scheme has subsequently been proposed, leaving wide open the question of whether near-optimal assortments can be computed in true polynomial time. The main contribution of this focused technical paper resides in closing these gaps by uncovering a striking independent-utility structure within Mallows choices, and turning this representation into a polynomial-time approximation scheme. Our central structural characterization explicitly constructs a single collection of mutually independent utilities, reproducing Mallows choice probabilities simultaneously for all offered sets. This exact choice equivalence connects pending Mallows-related challenges to the recent approximation framework of Bowers et al. (FOCS 2025) for assortment optimization under independent random utilities. We make this connection algorithmically feasible through a finite-support reduction that produces distributions of polynomial size while controlling revenue loss uniformly over all assortments. Fused together, these ingredients lead to an $O(n^{\tilde{O}(1/\epsilon^2)})$-time approximation scheme for assortment optimization under the Mallows model, while allowing arbitrary product prices, concentration parameters, and modal rankings.

We design an active reconfigurable intelligent surface (RIS) for acoustic multi-user multiple-input multiple-output (MU-MIMO) communication by solving a large-scale convex optimization problem, so that each emitter's broadband signal focuses in space and time at its intended receivers while crosstalk is suppressed. In acoustic experiments, we show that our approach outperforms existing time-reversal methods by 5.1-7.6 dB in crosstalk suppression, while achieving better temporal focusing.

In this work, we show that if $K$ is a nonempty, closed, bounded, and convex subset of $X$ and $1\leq \gamma<\sqrt{N(X)},$ where $N(X)$ denotes the Bynum normal structure coefficient, then every uniformly asymptotically Hölder $\gamma$-Lipschitz mapping $T\colon K\to K$ has a fixed point. To achieve this, it was necessary to guarantee the existence of a subsequence of a bounded sequence whose asymptotic diameter is controlled by the quantity $D(\{x_n\}),$ introduced by Jiménez-Melado, while simultaneously preserving the asymptotic radii at every point of the closure of the linear span generated by the original sequence. This allowed us to remove the Hölder exponent from the calculations and obtain a Hölder-type extension of the Casini–Maluta, Lim–Xu, and, consequently, Kim–Xu theorems.

Traffic density estimation from camera feeds requires connecting visual perception with short-horizon forecasting. We present a two-stage pipeline that combines vehicle detection and tracking with a spatial logic layer, followed by a temporal estimator. The spatial layer filters bounding boxes by their overlap with a precomputed road mask and extracts per-frame traffic features. LSTM, GRU, and Temporal Convolutional Network (TCN) estimators use these features to predict five future steps from a ten-frame input window. We benchmark ten detector variants from six families on a dataset of 5,716 annotated frames using a single NVIDIA GPU. YOLOv5l achieves the highest mAP@50:95 of 0.524 at 56 frames per second, while YOLOv8n reaches 258 frames per second at 0.487 mAP@50:95; these rates measure detector inference without tracking or spatial filtering. Temporal evaluation on 29,243 held-out windows yields aggregate R-squared values of 0.858 for GRU, 0.856 for LSTM, and 0.840 for TCN. These metrics measure forecasts of detector-derived telemetry and are dominated by direction variance, rather than establishing absolute traffic-density accuracy. No road mask was available for the evaluation stream, limiting validation of the spatial filtering component. A live run on a third camera stream examines forecasting behavior within the complete pipeline. The results characterize detector speed-accuracy trade-offs and the limitations of short-window traffic telemetry forecasting.

Position tracking is a well-studied problem in Euclidean navigation, yet comparatively little attention has been given to navigation on general manifolds, where motion is governed by the underlying geometry of the space. In this work, we formalize the problem of manifold navigation as a velocity-driven tracking task and propose a coordinate-chart-based learning framework in which learning models operate entirely in a Euclidean representation. Predicted trajectories are mapped to the manifold via an immersion function prior to error computation, allowing geometric consistency to be evaluated without explicitly enforcing manifold constraints during learning. Within this framework, we focus on Gated Recurrent Units (GRUs) for sequential position prediction on curved manifolds after comparisons with alternative recurrent architectures. We evaluate our GRU models, trained with pertinent custom loss functions, against both a standard MSE loss function and a naive vector-addition baseline. We evaluate our approach on both analytically (and numerically) defined manifolds, as well as a surface reconstructed from a LiDAR point cloud. Our results show that recurrent models can learn to approximate manifold-constrained dynamics from velocity sequences and consistently outperform Euclidean baselines. Our results demonstrate that certain custom loss functions significantly improve long-horizon prediction accuracy compared to conventional point-wise loss functions.