Papers

Projected Walk on Spheres (PWoS) solves surface PDEs through ambient sampling and closest-point projection, but tightly folded embeddings can force short steps or ambiguous projections despite simple intrinsic geometry. We introduce Walk-on-Ambient-Patch (WoAP), which treats the embedding as a solver variable. Edge-isometry constraints and tangent-point repulsion separate intrinsically distant regions, optionally in higher codimension; patch states track residual projection branches without introducing PDE boundaries. We analyze the resulting geometry–sampling tradeoff: additional dimensions provide separation freedom but reduce uniform tangent progress, while strong tangent-biased proposals incur large importance-weight moments. Folded-surface experiments demonstrate reduced projection conflicts, a separate hard-constraint pilot verifies metric preservation, and an internal fixed-RMSE comparison favors higher dimensions at stricter accuracy targets. Together, these results motivate choosing the embedding and projection state jointly with the stochastic solver.

Open-world mobile manipulation requires a robot to find an object, approach it, and move it to a target receptacle from a language instruction. Training vision-language model (VLM) agents for these tasks requires demonstrations of both action selection and active vision. Existing pipelines often convert planned trajectories into high-level action labels, but shortest-path progress provides limited supervision for deciding where to look. We introduce Agent-Interface Data Alignment (AIDA), a data collection pipeline in which a teacher directly selects and executes actions through the deployed agent's skill interface. For mobile manipulation, we design teachers that maintain target visibility, recover lost targets, and approach for picking or placing. We add template-based spatial reasoning supervision and use a shared harness to organize observations, history, and outputs during training and inference. The resulting agent, AIDA-OWMM, achieves 71.76% full-task success on 170 held-out OWMM episodes. Teacher sensitivity analysis shows that active-vision demonstrations improve student success. The simulation-trained agent achieves 38% end-to-end success on a real mobile robot without additional training. Applying AIDA to a navigation subset of EmbodiedBench further demonstrates the pipeline's utility for navigation tasks.

In this work, we propose a transfer learning algorithm for covariate shift, integrating sample reweighting with representation learning. A key feature of our approach is the use of a lower-dimensional latent space for modeling, in contrast to conventional methods that operate directly in the high-dimensional ambient space. Our method estimates the density ratio of learned latent features for downstream weighted prediction. We establish explicit target-domain excess-risk rates with independent data folds for strictly sufficient learned representations with regular learned-space prediction scores and density ratios. We give dimension comparisons under stated smoothness conditions and a variance comparison for true weights and a fixed predictor. General finite-sample inequalities retain representation-quality errors. Experiments on simulated and real-world datasets demonstrate gains from combining learned representations and latent weighting, and reveal sensitivity to initialization and domain choice.

Settling one comparison between two truncation samplers has cost six thousand A100-hours, and nothing says in advance how far apart two samplers can be. We observe that almost every deployed truncation rule keeps a prefix of the probability-sorted vocabulary, so any two such rules are nested at every decoding step. Nesting yields a closed-form per-step distance and a coupling under which both samplers emit identical text until they first disagree. Accumulated over a generation, this gives a separation certificate that bounds the difference between two samplers on any bounded outcome, is computable from logs a comparison already produces, and equals their sequence-level total variation distance exactly when neither rule ever overtakes the other. Two consequences follow without measurement: exactness is fragile, and certifying a small difference requires the two retained masses to agree to very high precision at every step. On six open-weight models over four math and science benchmarks, the certificate for every hyperparameter grid we tested is at least 0.998, so a bound alone rarely settles a comparison, although two members of one family can be far closer. What remains useful is the coupling, which gives an unbiased paired estimator that cuts variance $1.2$-$3.8\times$ against prompt-level pairing. Read against benchmark sizes at the default pair's variance and our point estimate of its between-prompt component, resolving a one-point difference needs 8 to 32 samples per prompt on GSM8K, MATH-500 and GPQA-Diamond and about 210 on AIME 2025; at that component's upper confidence bound GPQA-Diamond needs more than 32 and AIME 2025 cannot be resolved at any sample count. Choosing a truncation sampler is a measurement problem at least as much as a design one. The code is available at https://github.com/KurbanIntelligenceLab/truncation-samplers.

We present a comprehensive broadband spectro-temporal analysis of the dynamically confirmed Galactic black hole transient GS 1354-64 during its 2025-26 outburst, using near-simultaneous observations from Insight-HXMT and XRISM. The high spectral resolution of the XRISM-Resolve microcalorimeter, coupled with the high-cadence broadband coverage of Insight-HXMT, reveals a dramatic evolution in the inner accretion geometry. During the early hard-intermediate state, the spectrum was dominated by a hot Comptonizing corona accompanied by relativistically broadened reflection features. As the outburst progressed, the corona cooled efficiently, the photon index steepened (Gamma >~ 2.5), and the reflection signatures, including the broad Fe K-alpha emission, were quenched, yielding a featureless, disk-dominated continuum. Concurrently, Type-C quasi-periodic oscillations (QPOs) evolved from 0.25 Hz to 6.52 Hz. Cross-spectral timing analysis revealed that the broadband X-ray time lags changed from pronounced positive (hard) delays (~160 ms) at low frequencies to near zero as the source softened. However, a statistical analysis incorporating the measurement uncertainties shows that the broadband lags lack a significant monotonic correlation with the QPO frequency, photon index, or fractional rms. Instead, the scattered lag behavior suggests a competition between positive Comptonization delays and negative thermal reverberation. While the spectral softening and QPO acceleration provide strong evidence for a geometric contraction of the corona (whether interpreted via Lense-Thirring precession or the Two-Component Advective Flow (TCAF) paradigm), the broadband timing properties underscore the turbulent and inhomogeneous nature of the inner flow as the advancing Keplerian disk drives the source into the soft state.

We study dynamical chiral symmetry breaking in $(2{+}1)$-dimensional QED on a rigidly rotating disc, $\Omega R<1$, within the rainbow Schwinger–Dyson framework. At zero temperature the rotation response of the condensate vanishes identically, so $N_c^{\rm SD}(\Omega,T{=}0)=N_c^{\rm SD}(0)=2.60\pm0.01$ (using three operational definitions). At finite temperature, rotation suppresses the condensate through a dominant occupation-reweighting channel, $\hat{\kappa}_{\rm occ}=-1.55$, accounting for $\ge 99.995\%$ of the linearized total response at the reference parameters, with self-consistent feedback amplifying it by $26.5$. The screening channel is reported at fixed regularization, $\hat{\kappa}_{\rm scr}(\varepsilon = 0.01)=-0.97$; its $\varepsilon \to 0$ behavior is logarithmically divergent. The crossover flavor $N^{*}(\Omega)$ falls monotonically at fixed temperature (a corollary). The critical flavor number is unchanged by rotation at $T=0$ (theorem). Together these results set the finite-temperature reference for the model.

Reviewers sometimes name existing repository items outside the change under review. We ask whether such references are more common in larger repositories, and whether the pattern differs between agent-authored and human-authored pull requests. An instrument resolves names in inline review comments against the base-commit repository; size-matched negative controls estimate chance matches. Among 92,042 comments on agent pull requests in 2,034 GitHub repositories, 6.5 per cent name an existing item outside the change. An internally pre-specified log-linear model finds an odds ratio of 1.35 per tenfold increase in code files (interval 1.15 to 1.59), and size-matched negative controls indicate that chance matching does not account for the rise. Exploratory analyses suggest that the association is concentrated from small to mid-sized repositories and is imprecise among large ones. Human pull requests in 1,845 of these repositories show a similar association. A pre-specified comparison finds a small agent excess just within the bound set as negligible, but the evidence does not establish a robust agent-specific difference. The instrument misses many references, so reported shares likely understate prevalence, and the validation cannot estimate how recall changes with repository size.

The telecommunications industry is shifting toward an experience-driven era defined by immersive applications that impose stringent network demands. While passive optical network (PON)-based Fiber-To-The-Home (FTTH) architectures have historically delivered high-capacity broadband, a growing performance gap between access and indoor networks necessitates driving fiber deeper into premises. Complementing existing copper and WiFi technologies, Fiber-to-the-Room (FTTR) is emerging as a critical enabler. This article examines the drivers of this architectural shift, specifically focusing on collaborative extended reality (XR). We analyze the multi-modal traffic characteristics and Quality-of-Experience (QoE) requirements of XR, alongside the resulting network performance implications. To address these demands, we propose a novel resource allocation framework integrating coarse-grained traffic forecasting with intelligent in-premise roaming. This framework facilitates the flexible deployment of artificial intelligence models tailored to the computational capabilities of the FTTH, FTTR, and WiFi segments. Numerical evaluations of a representative multi-tier network demonstrate that long-horizon, multi-step-ahead traffic forecasts significantly reduce inference frequency. This approach enables coordinated resource allocation and network-orchestrated seamless mobility across rooms, effectively satisfying collaborative XR QoE requirements. Finally, we highlight strategies to amortize FTTR capital expenditure by extending the optical infrastructure's role beyond basic connectivity. By supporting diverse services over a unified physical layer, FTTR enhances infrastructure utilization, unlocks novel revenue streams, and maximizes the value of in-premise fiber deployments.

Recent multimodal large language models achieve promising results on visual reasoning tasks, approaching human-level performance on existing STEM benchmarks. However, these capabilities degrade under complex real-world scenes. We identify that chain-of-thought reasoning remains largely confined to the linguistic space, rarely anchoring each step in visual evidence. The main cause is the absence of such data during training. In this work, we introduce a training data augmentation pipeline, Visual Augmentation Primitives (VAP), which leverages state-of-the-art vision generative models to synthesize diverse photorealistic training samples and corresponding reasoning text. VAP introduces some basic operators and applies them to a seed image and gets a variant. It also constructs coherent multimodal reasoning chains throughout the generation process. Such training data force models to perceive visual content and perform logical reasoning according to them at every step. We further introduce multimodal chain-of-thought rubric-based reinforcement learning to enhance this. It rewards not only text reasoning but also visual reasoning by scoring intermediate reasoning steps for logical validity, completeness, and consistency. Moreover, we construct the UNREAL benchmark to systematically evaluate visual reasoning on hyperrealistic scenes across controllable difficulty levels. Experiments show that a 4B model built on this framework surpasses 8B baselines, with performance improving consistently as the model scales to 32B, validating the scaling law for visual reasoning.

We introduce UNISON, a unified framework that bridges multiple instance learning and recommendation systems by treating both as instances of learning from scored bag collections of (item, score) pairs. Unlike traditional approaches that address bag-level classification and personalized recommendation as separate problems, UNISON decomposes learning into three interconnected stages: (1) learning universal item representations, (2) modeling bag-specific preference patterns through lightweight personalized parameters, and (3) inferring bag-level characteristics from learned preferences. We justify the architectural choice of linear bag-specific scoring through a first-order analysis: when item embeddings are sufficiently smooth in the score, a linear function approximates the score up to a Taylor remainder controlled by the curvature of the underlying preference function. For cold-start scenarios, we show that the cold-bag fitting problem reduces to ridge-less linear regression with a closed-form solution, and provide convergence guarantees for the iterative variant. Empirically, UNISON matches or outperforms state-of-the-art approaches across diverse domains: entertainment (books, movies), immunology (T cell receptor (TCR) based classification), and microbiome, offering superior computational efficiency and interpretability. A controlled synthetic experiment further confirms that the bag-specific parameters ($w_j, b_j$) recover the latent factors that drive item scores even when the projection $\phi$ has no access to the original scoring mechanism (AUC > 0.998). UNISON is available at https://github.com/louzounlab/UNISON.

Soft wearable robots must commit to assistance around movement onset, when the available signals are ambiguous. Surface electromyography (sEMG) detects neuromuscular drive early but degrades under sweat and electrode shift, and kinematic sensors respond only once the limb moves. This letter presents a knitted textile interface that co-samples a three-channel mechanomyography (MMG) array and an anterior strain sensor on a single synchronous 500 Hz clock. Across five participants, MMG activation preceded strain-detected knee motion during sit-to-stand by per-channel medians of 322-344 ms. Sampled on the same clock, the sign of the strain slope resolved movement direction on 649 of 650 completed transitions with no training or per-participant calibration, raising four-class balanced accuracy from 90.3% to 95.6%. The fused signals drove a two-stage confirm-then-assist policy for a soft pneumatic knee. Across 240 trials in four participants, the onboard controller entered the assist state on 78 of 80 sit-to-stand trials and on none of the 80 isometric co-contractions. It also entered the assist state on 27 of 80 stand-to-sit trials and left it at the hold timeout, motivating an antagonistic flexor gauge to resolve this direction at onset. Co-sampling muscle acoustics with textile strain on one clock lets the inflation command be issued around movement onset.

Large-scale video generation models are increasingly viewed as a promising path toward world models, yet their ability to capture causally coherent physical dynamics remains poorly understood. Existing evaluations largely emphasize visual quality, prompt adherence, or broad physical plausibility, leaving open whether a model can faithfully realize a complete causal cascade, in which an initiating event propagates through causally dependent interactions to a terminal outcome. We introduce CausalCascade, a simulator-grounded benchmark centered on 50 event-rich Blender scenes with structured event graphs, graph-grounded diagnostic VQA, three levels of future-event specification, and 2,832 controlled counterfactual variants, and use it to evaluate nine image-to-video models with complementary motion-, event-, and counterfactual-level diagnostics. Across the evaluated models, generated motion is more reliably localized spatially than realized with correct spatiotemporal evolution, while richer future-event specification improves event recovery but leaves physical realization limited. Counterfactual evaluation further reveals weak selective responsiveness to physical interventions, while most audited failures are foundational, arising at scene consistency or event occurrence. Together, these results position causal cascade generation as a process-level test of world modeling and highlight the need to jointly recover the intended future, faithfully realize its physical evolution, selectively respond to physical interventions, and maintain a coherent physical world over time. Code and dataset are available at https://github.com/SJTU-DeepDeltaLab/CausalCascade .

A unified framework is proposed to compute a neoclassical equilibrium for tokamaks with non-axisymmetric magnetic perturbations, based on a Hamiltonian description combined with a variational approach that relies on a principle of minimum entropy production. This approach allows for a transparent identification of the respective contributions from different classes of trapped particles in magnetic well minima. Analytic expressions are derived for specific collisionality regimes, and a fast and efficient numerical procedure is devised to compute the entropy production rate. Finding the extremum of the entropy production leads to tractable expressions of transport coefficients that can be computed quickly and efficiently.

Existing navigation systems commonly rely on dedicated depth sensors or explicit depth reconstruction, while learning to generate trajectories directly from RGB images remains challenging due to the sim-to-real domain gap. In this work, we propose Stereo-Planner, an end-to-end vision-to-trajectory framework that enables zero-shot sim-to-real planning from stereo RGB observations. The key idea is to formulate trajectory generation as state- and scale-conditioned querying of latent stereo geometry. A Scene Representor incorporates a pretrained vision grounding foundation model to extract geometric cues shared across simulated and real-world environments, supporting generalization across visual domains. A lightweight Trajectory Decoder then translates these representations into trajectories through interleaved attention, separating trajectory-state interaction from scene-feature retrieval and incorporating the stereo baseline as a metric-scale cue. With these designs, Stereo-Planner is trained entirely on simulated data by minimizing differentiable trajectory costs and deployed directly in real-world environments without fine-tuning. Benchmark results demonstrate strong cross-scene generalization, with a 95% success rate in simulation environments at a commanded speed of 8 m/s, and competitive performance against depth-based planners using only stereo RGB observations for scene perception. Furthermore, deployment on a compact quadrotor equipped with an NVIDIA Orin NX enables autonomous flight at speeds of up to 7 m/s, with a mean onboard vision-to-action inference time of 24.27 ms. The software, simulation environments, and hardware designs will be open-sourced at https://github.com/Stereo-Planner/Stereo-Planner.

Let \(E(X)\) count the even integers between \(4\) and \(X\) that are not sums of two primes. We combine Pintz's explicit formula for the major arcs with the exponential-sum estimate of Maynard, Pandey, and Radziwiłł to prove \(E(X)\ll_\varepsilon X^{7/12+\varepsilon}\) whenever all Dirichlet \(L\)-functions have a common fixed zero-free half-plane \(\Rea s>\theta_0\), with \(\theta_0<1\). The uniform \(7/8\) theorem reported in the OpenAI mathematics release supplies this input. Under the stronger hypothesis that every nontrivial Dirichlet zero has real part at most \(\theta\), where \(1/2\leq\theta\leq2/3\), we prove \[ E(X)\ll_{\theta,\varepsilon}X^{g(\theta)+\varepsilon}, \qquad g(\theta)=\frac{\theta(5-4\theta)}{2(2-\theta)}. \] Thus every fixed \(\theta<2/3\) gives an exponent strictly below \(7/12\). The latter argument uses a classical fixed-modulus zero-density estimate and is independent of the new exponential-sum theorem.

Visual self-modelling lets robots learn body models from observations, but such models usually encode kinematics implicitly rather than exposing metric joint parameters for computation and control. Moreover, a good fit to images does not by itself establish accurate kinematics. Here we present an explicit analytic robot self-model that requires neither deformation networks nor URDF/CAD templates. Multi-view images and joint readings establish Gaussian appearance and provide motion evidence for rigid link assignments, whereas sparse end-effector poses independently identify metric screw axes. The resulting closed-form forward kinematics and analytic Jacobian can be evaluated beyond the fitting ranges. We validate the model on a simulated seven-axis arm, a simulated twelve-joint quadruped and a real six-axis arm. In simulation, it achieves millimetre-level reaching and pick-and-place, as well as closed-loop quadruped walking. On the real arm, it renders held-out configurations, predicts end-effector positions with a median error of 6.4 mm, compared with 11.7 mm for a calibrated nominal model, and supports reaching with external marker feedback. A controlled comparison shows that image fit alone is not enough: two Panda models differing only in their joint axes are 0.55 dB apart in PSNR, yet their end-effector prediction errors differ 13.7-fold.

The extension of the LUX–ZEPLIN nuclear-recoil analysis to approximately $270\,\mathrm{keV}$ probes a qualitatively new dark-matter regime in which endothermic scattering can suppress conventional low-energy recoils and concentrate the surviving spectrum near the Galactic high-velocity tail. We construct a modular-$S_4$ realization in which a minimal $2N_R+2S$ inverse seesaw accounts for lepton flavor, while a separate pair of Standard-Model-singlet fermions forms the pseudo-Dirac state relevant for high-recoil xenon scattering. The sectors share a common complex modulus $\tau$, so the modular forms selected by charged-lepton and neutrino data also enter the operators generating the dark Dirac mass and Majorana splitting. Our scan yields $181447$ lepton-sector solutions satisfying $\chi^2_{\ell+\nu}<30$, distributed among several disconnected modular regions, and predicts one effectively massless light neutrino at leading order. Restoring the physical scales allows TeV-scale heavy quasi-Dirac neutral fermions with small non-unitarity. We subsequently scan $2\times10^6$ dark-sector points only over flavor-accepted values of $\tau$ and identify common-modulus solutions in the LZ-oriented region $300\,\mathrm{GeV}\le m_\chi\le2\,\mathrm{TeV}$ and $300\,\mathrm{keV}\le\delta\le400\,\mathrm{keV}$. An exploratory two-bin Poisson likelihood, including endothermic xenon kinematics, the Helm form factor, Standard-Halo-Model velocities, Gaussian energy smearing, and profiling over the signal normalization, gives a best grid point at $(m_\chi,\delta)\simeq(1.847\,\mathrm{TeV},371.5\,\mathrm{keV})$, close to the terrestrial inelastic kinematic ceiling. The construction provides a direct link between modular lepton flavor, TeV-scale inverse-seesaw dynamics, and high-recoil inelastic dark matter.

Vision-Language-Action (VLA) models commonly generate robot actions token by token through Large Language Model (LLM) decoders, causing inference latency to grow with action sequence length and limiting closed-loop control frequency. We present Goal-Conditioned Vision-Predictor-Action (VPA), which replaces autoregressive decoders with a lightweight latent control loop. A shared vision encoder and a frozen text encoder embed observations, goal images, and instructions; a neuro-symbolic selector chooses a discrete skill; a Joint-Embedding Predictive Architecture (JEPA) predictor forecasts the next latent state; and a flow-matching solver generates an entire action chunk in a few integration steps, so that sequential network evaluations per decision step do not depend on the action horizon. We analyze inference complexity, regularization against representation collapse, and conditions under which latent sub-goal thresholding limits error accumulation across task phases. As an initial proof of concept, we evaluated VPA on the LIBERO-10 suite. The trainable model has under 20M parameters (checkpoint under 75 MB, excluding a frozen 63.4M-parameter CLIP text encoder); a decision step of a single-camera reference configuration takes 10-14 ms on an Apple M4; and trained only on LIBERO-10 demonstrations in under three hours on a single GPU, a two-camera policy succeeded in 40.0% of 200 evaluation episodes. These preliminary results from a single training run suggest the approach is workable. Code and weights are available at https://github.com/ylee-sling/Vision-Predictor-Action and https://huggingface.co/ylee-sling/vpa-libero10, and archived at https://doi.org/10.5281/zenodo.22960920.

Training-free story visualization without reference images must preserve recurring entities across frames while scaling to long narratives. Existing methods typically maintain consistency by conditioning each frame on other frames of the same story, coupling generation time, VRAM, or both to story length. We introduce ELECT, which instead settles cross-frame identity before final rendering through a language-guided scene-entity mapping and stationary anchors elected from the model's own drafts. This makes the per-frame cost of the final rendering pass independent of story length. Joint attention exceeds 96 GB of VRAM at 32 scenes, whereas ELECT remains at 8.3 s per frame and under 20 GB VRAM from 10 to 1000 scenes. On the Story50 long-story benchmark, ELECT reaches 0.833 average Character Consistency Similarity (aCCS), compared with 0.826 for ten-round refinement, at one seventh of its generation cost, with lower text alignment (0.327 vs. 0.340). At 1000 scenes, to our knowledge, the first evaluation of training-free story visualization at this length, ELECT exceeds ten-round refinement by 0.017 aCCS and the nearest flat-cost baseline by 0.091, while also surpassing refinement in text alignment at one twenty-fourth of its generation time. These results show that long-horizon consistency need not require increasingly expensive inter-frame conditioning as stories grow.

Catalytic computation involves the study of Turing machines that are provided an additional catalytic tape (with arbitrary content) that the machine may use while ensuring that the tape contents are restored at the end of the computation. Although it is known that catalytic log-space machines are at least as powerful as non-deterministic log-space (and more), we do not have unconditional asymptotic separations. In this work, we prove an unconditional separation between a deterministic space complexity class and its catalytic counterpart. More precisely, at the doubly logarithmic scale, we show that catalytic Turing machines can provably compute more languages than standard deterministic doubly-logarithmic space machines. The separation is witnessed by the unary language $\mathrm{POW2} = \{1^n : n \text{ is a power of two}\}$. We construct a catalytic Turing machine that uses $O(\log \log n)$ bits of space and $O(\log n)$ bits of catalytic tape to decide $\mathrm{POW2}$, whereas any standard deterministic Turing machine requires $\Omega(\log n)$ space to decide it.

Model averaging emerges as an attractive ensemble technique that strategically synthesizes all available information from potential candidate models to enhance estimation accuracy. Despite of having been widely practiced in various areas in biostatistics and economics, its application to causal inference is rather limited. We propose to estimate the average treatment effect (ATE) by forming the weighted combination of the robust rank-based estimators obtained from a series of candidate models, where the model weights, selected via the growing window cross-validation, dynamically adjust the importance of candidate models. The proposed robust rank-based model averaging (RRMA) is not only robust to handle potential outliers and heavy-tailed error distributions but also capable to reduce the risk of model mis-specification and enhance the flexibility and the accuracy of estimation. Theoretically, we establish the desirable asymptotic properties of RRMA, including the asymptotic optimality, consistency and asymptotic distribution. Moreover, motivated by the asymptotic distribution of RRMA, an easy-to-implement confidence interval is also developed for the ATE. Simulation experiments and an empirical application demonstrate the superiority of RRMA over existing competitors in estimation accuracy, coverage probabilities and widths of confidence intervals.

A covalent polymer network is orders of magnitude weaker than individual covalent bonds. This large gap reveals an unrealized potential. The weakness of a network comes not from individual covalent bonds, but from how they are connected. Here we unlock this potential by identifying a topological criterion, involving optimally sparse crosslinks, long chains, and dense entanglements. Optimizing each topological variable alone is insufficient for high strength, yet exceptional strength emerges when they are combined within a narrow regime. We describe the physics of this synergy, and use the criterion to strengthen networks widely used but known to be weak. For example, we prepare a polyacrylamide hydrogel of 90 wt% water, amplifying strength from a commonly reported value of ~0.1 MPa to ~6.5 MPa. The exceptional strength is achieved without sacrificing other properties, such as softness, toughness, and elasticity. The criterion establishes topology as a general design principle for strong polymer networks.

Using the geometric realization spectral sequence and the Serre spectral sequence, we compute $K_1(\operatorname{Mat}_*)$, the first K-theory group of the proto-exact category of pointed matroids, answering a question of Jun, Sistko and Wright.

We give the topological classification of some simplest univariate complex fewnomials, and find tropical fans of the fewnomial strata with each topological type. Specifically, for the support $ A=\{d,d+1,d+2,d+3,d+4\},\quad d\geq3, $ we classify the topological equivalence classes of polynomials having two critical values of ramification type $(2,2)$. There is one class for odd $d$ and two classes for even $d$. We describe the branches at infinity of the corresponding one-dimensional stratum using Newton polytopes of certain complete intersection representations of the sought strata, and determine their tropicalizations. The combinatorial types of the obtained tropical polynomials distinguishes all three kinds of topological equivalence classes. These computations suggest a correspondence between topological equivalence classes of polynomials and combinatorial types of tropicalizations of their branches at infinity, as well as a possible periodicity phenomenon under translations of the support.

We study the mean-squared error (MSE) rate-distortion function (RDF) of finite Gaussian mixture models (GMMs) in $\mathbb{R}^d$, for which neither the RDF nor an optimal test channel is known in closed form. It can be sandwiched between the genie-aided conditional RDF $R_{\mathbf{X} | T}(D)$, which can be characterized in closed-form for a GMM, and $R_{\mathbf{X} | T}(D)+I(\mathbf{X};T)$, where $T$ denotes the latent component label. We show that the upper bound can be achieved operationally by the proposed Gibbs-relabelling method (GRM), which conveys a label from the posterior $P_{T|\mathbf{X}}$ through channel simulation at rate $I(\mathbf{X};T)$, followed by vector quantization of the resulting exactly Gaussian conditional sources by reverse water-filling. Using the Shannon lower bound (SLB), we prove that GRM attains the SLB, and hence the RDF, of a general finite mixture if and only if every component attains its own SLB. For a GMM this holds throughout the fully active interval $D/d<\min_{k,m}\lambda_{k,m}$, where $\lambda_{k,m}$ are the eigenvalues of the component covariances, and for scalar GMMs the condition is also necessary. Since GRM cannot operate below the label cost $I(\mathbf{X};T)$, we propose a complementary stochastic scalar quantization (SSQ) scheme for low rates, which simulates an $M$-ary reconstruction index. We show that at low rates SSQ with $M\geq 2$ matches the Shannon RDF to first order: $R(D_{\max}-\delta)=\delta/(2\tau^2)+o(\delta)$, where $\tau^2$ is a directional sub-Gaussian proxy of the mixture, and quantify the price of a finite codebook through a strict rate gap at high rates and a distortion floor whose joint scaling in $M$ and number of mixture components is characterized. Numerical results illustrate both regimes and the finite-blocklength cost of channel simulation.

Quadruped robots deployed for inspection and field missions must cross heterogeneous terrain, from stairs, slopes, and gaps to high platforms, stepping stones, and balance beams, where safe support is sparse or see-through. Existing methods interpose a terrain map or a depth image between sensing and control. Maps are costly to maintain, corrupted by odometry drift and outliers, and misled by see-through gratings, while depth cameras degrade with lighting and surface material. In this paper, we present PointWalker, a mapless framework whose single reinforcement learning policy directly consumes raw point clouds from four light detection and ranging (LiDAR) sensors. Voxelized points are encoded by linear self-attention and fused with proprioception through cross-attention, so terrain geometry reaches the policy without maps or foothold estimation. One proximal policy optimization (PPO) run, with terrain-aware rewards and dual-channel simulation of see-through gratings, yields one policy for all seven terrain classes with a 90.1% mean success rate in simulation. Deployed zero-shot on a Deep Robotics X30 at 50 Hz onboard, it crosses 0.8-m gaps, climbs 0.8-m platforms and 45{\deg} steel-grating stairs, carries a 50-kg payload, and completes a 2.5-km mountain route.

Distributed-input distributed-output (DIDO) systems arise in numerous engineering applications where large numbers of actuators generate spatially distributed physical fields that are monitored by distributed sensors. Developing physically interpretable models that enable real-time optimal control of these systems remains challenging because of the high dimensionality and strong spatial coupling between inputs and outputs. In this work, we propose a physics-based framework for modeling and closed-loop optimal control of DIDO systems from experimental input-output data. First, an effective partial differential equation (PDE) is selected among candidate transport models and discretized on the actuator grid to obtain a minimum-grid representation. Second, the PDE is solved in closed form, which yields an input-output operator with only four physically interpretable parameters. Third, the operator is incorporated into an iterative, constrained quadratic program that accounts for the actuator limits. The framework is demonstrated on the inner 40 x 40 section of the world's highest-resolution Fan Array Wind Generator (FAWG), comprising 1600 independently controlled fans with 36 distributed velocity measurements. The model describes the spatial interaction between the 1600 actuators and the measured velocity field with normalized mean absolute prediction errors of 11-20% for representative actuation patterns. The closed-loop controller reproduces all three prescribed two-dimensional velocity fields with a normalized mean absolute error below 2.3% in fewer than 10 iterations.

The local Hilbert space dimension is a fundamental parameter in quantum many-body systems, but its role in controlling the ergodicity-breaking transition remains less explored. We systematically study this question by introducing toy models of qudits in zero dimensions that exhibit an ergodicity-breaking transition. Using the hybridization condition, we analytically obtain the dependence of the critical value of the interactions on the local Hilbert space dimension. Numerical studies of spectral correlation measures show agreement with the theoretical predictions, hence confirming the existence of the ergodicity-breaking transition in these models. We further introduce a distinct higher spin version of the model and numerically obtain the same critical behavior, demonstrating that the observed critical point is independent of the microscopic structure of interactions considered.

Nonlinear Constrained Optimisation (NCO) requires simultaneous satisfaction of the Karush-Kuhn-Tucker (KKT) conditions. Existing methods enforce these conditions through projections, penalties, barriers, or sequential approximations, potentially introducing computational complexity and convergence difficulties. For nonconvex problems, a KKT point need not be a local optimum. This paper reformulates NCO as stabilisation of a unified KKT sliding residual manifold and develops SM-KKT, a projection-free solver. Stationarity, equality feasibility, and regularised Fischer-Burmeister complementarity are integrated into a unified residual system, with complementarity encoding inequality feasibility, dual feasibility, and complementary slackness. The manifold's zero set is shown to be equivalent to the KKT conditions. The required Jacobian saddle-point inertia is characterised and shown, under stated assumptions, to be equivalent to the simultaneous satisfaction of the Linear Independence Constraint Qualification (LICQ) and Second-Order Sufficient Condition (SOSC). This characterisation establishes local stability of the structured correction algorithm under these conditions and distinguishes nondegenerate locally optimal KKT solutions from points failing second-order optimality. SM-KKT computes structured primal–dual corrections and applies a discrete sliding reaching law to drive the KKT residual into a prescribed boundary layer in finite time. Four nonlinear benchmarks show recovery of reference constrained optima with KKT residuals below $10^{-6}$, earlier boundary-layer reaching, and favourable KKT accuracy compared with projected primal-dual, augmented-Lagrangian, quadratic-penalty, and log-barrier baselines.

We investigate the factors affecting salience in movie screenplay by posing two research questions: 1. Does Uniform Information Density (UID) predict salient scenes? 2. What other linguistic properties distinguish salient scenes from non-salient background? We answer both questions through a controlled corpus study on the MENSA corpus, paired with a Linguistically-Grounded Salience Model (LGSM), a dual-stream classifier that fuses a frozen BERT encoder with explicit linguistic features through adaptive gating. The UID picture is layered in long-form discourse. Per-scene UID summaries carry no independent signal once length is controlled, but at the token level salient scenes match non-salient material in the bulk while specifically suppressing the rarest, hardest-to-predict tokens in the upper tail. UID therefore lives at the within-scene token level rather than as a per-scene aggregate. Salient scenes also show a moderate and sustained cast of central characters (following an inverted-U pattern), strong third-person usage, syntactically simpler language, and more abstract vocabulary about motivation and conflict. LGSM exploits this signature and improves recall on salient scenes over a strong semantic baseline while yielding better downstream summaries.