Papers

We investigate the electromagnetic field produced by a harmonically oscillating point charge and measured by a spatially separated observer undergoing the same motion. We evaluate the exact retarded field on the observer's worldline and project the electromagnetic field tensor onto the observer's local orthonormal tetrad. This construction yields the electric and magnetic fields, electromagnetic energy density, and Poynting vector measured as functions of the observer's proper time. Our formulation separates unambiguous local observables from the observer-dependent classification of a field as radiation and provides a concrete setting in which to examine how a charge that is spatially static in a non-inertial coordinate system can nevertheless produce time-dependent locally measured fields.

Forecasting future 3D occupancy from surround-view cameras is essential for autonomous driving, yet existing approaches rely on dense voxel or bird's-eye-view representations whose cost grows rapidly with spatial resolution and prediction horizon. Because these representations do not explicitly maintain object identities, they also struggle to preserve instance consistency over time. We present LighTROcc, a lightweight instance-centric framework that represents movable objects with a compact set of learned queries and predicts present and future occupancy in a single forward pass. LighTROcc localizes each query through attention-guided forward lifting, combining image-space cross-attention, query-specific depth, and camera geometry to estimate its 3D center. Each instance is modeled as a mixture of anisotropic 3D Gaussians and propagated across future steps using predicted displacements, producing continuous, temporally consistent occupancy forecasts. Experiments on nuScenes and supplemented nuScenes-Occupancy show that LighTROcc outperforms the evaluated dense and instance-wise baselines in instance-level forecasting accuracy while maintaining strong voxel-level occupancy quality. Across different model configurations, LighTROcc achieves a favorable balance between forecasting accuracy and computational efficiency, demonstrating the potential of compact instance-centric modeling for camera-based 4D occupancy forecasting.

A $k$-bend path is a non-self-intersecting polyline that lies on a grid and consists of at most $k+1$ axis-parallel line segments. An $\llcorner$-EPG graph is a graph whose vertices can be represented by 1-bend paths on a grid, where each path is either $\llcorner$, $\shortmid$, or $\text{-}$, such that two vertices are adjacent if and only if the corresponding paths share at least one grid edge. Characterizing chordal $\llcorner$-EPG graphs was explicitly posed as an open problem by Cameron, Chaplick, and Hoàng. We resolve this by giving two equivalent characterizations of connected chordal $\llcorner$-EPG graphs. The first assigns to every connected chordal $\llcorner$-EPG graph an ordered clique partition tree of its vertex set, where the underlying tree is the bipartite incidence graph of the horizontal and vertical edge-intersection components. The second is stated purely in terms of maximal cliques: a connected chordal graph is $\llcorner$-EPG if and only if some clique tree admits an admissible partial orientation. A reduction lemma replaces local clique labels by maximal cliques, linking the two characterizations. For a prescribed clique tree, the existence of an admissible partial orientation reduces to 2-SAT and is decided in $O(nM^2)$ time, where $n$ and $M$ are the numbers of vertices and maximal cliques. Finally, we show that strong chordality is not sufficient: we exhibit a strongly chordal graph that is a minimal forbidden induced subgraph for $\llcorner$-EPG, and a family of split graphs with a unique clique tree for which membership in $\llcorner$-EPG reduces to a neighborhood condition.

Restorative control seeks lasting recovery through an intervention that ends in finite time. We formulate this objective as a reach-avoid problem in which the input must bring the system safely into a desired basin of attraction before withdrawal. Two candidates share bistable baseline dynamics but accumulate irreversible damage through different allocations of drive-generated exposure. We derive a lower bound on the exposure required for basin transfer and a sufficient construction for safe restoration. When the lower bound exceeds the summed tolerances, every common open-loop input that restores either model causes failure under at least one. With sufficient tolerance, proportional allocation restores both without identification. For feedback from output samples with Gaussian noise, we bound safe-restoration probability in terms of failure risk under the alternative model. A numerical example illustrates the certificates under two sensing regimes.

Microsatellite instability-high (MSI-H) and high tumor mutational burden (TMB-H) are clinically relevant biomarkers, yet their histopathological prediction remains challenging when models are transferred across morphologically distinct cancer types. Immune-associated spatial patterns can persist across cancers despite these morphological differences, but foundation-model-based predictors trained on a single cancer do not explicitly use this information, limiting cross-cancer generalization. To address this limitation, we propose TIRA (Tumor Immune Representation Adaptation), a target-free framework that refines frozen foundation-model representations using spatial immune topology, without requiring target-domain data during model development or test-time adaptation. TIRA uses a topology-supervised biology representation to condition tile-level attention while pooling only morphological features for joint MSI and TMB prediction. We train TIRA on TCGA-COAD+READ and evaluate it zero-shot on CPTAC-COAD, TCGA-STAD, TCGA-UCEC, and CPTAC-UCEC, covering cross-site, cross-cancer, and combined cross-cancer-site distribution shifts under UNI2, CONCH, and Virchow2. With UNI2, TIRA improved zero-shot AUROC on TCGA-STAD from 0.633 to 0.766 for MSI and from 0.651 to 0.772 for TMB. Source-derived spatial immune topology improved the cross-cancer robustness of frozen pathology foundation-model representations.

Pre-trained vision encoders contain layer-wise visual representations that differ in spatial granularity, semantic abstraction, and sensitivity to local details. However, most Multimodal Large Language Models (MLLMs) rely on only the final or penultimate vision encoder representations or fixed aggregation rules, making visual abstraction largely query-agnostic and limiting access to fine-grained cues such as small objects, spatial details, text, and subtle visual attributes. In this work, we propose Mixture of Layers (MoL), an instruction-conditioned layer routing approach at the visual patch level that dynamically aggregates query-relevant latent representations from intermediate vision encoder layers. Given a text query, MoL predicts routing probabilities over vision encoder layers and performs a top-k sparse aggregation over selected hidden states at either the image level, patch level, or through a hybrid routing mechanism. In doing so, MoL enables query-adaptive access to layer-specific visual features for fine-grained visual reasoning. Our experiments across 7 fine-grained visual reasoning tasks demonstrate substantial performance improvements, especially across fine-grained visual grounding and understanding tasks such as +18.9% improvement on V* in overall accuracy, +4.5% on HRBench4K, and +16.3% on CharXiv compared to the baseline MLLMs, without resorting to multi-resolution inputs, simple interleaving of multiple vision encoders, or increasing the number of patch tokens. We study vision encoders' receptive field scales across different layers and their sampling behaviors to provide an in-depth analysis of why layer-wise sampling is helpful, demonstrating that conditional visual representations are a key step towards better visual perception and reasoning in MLLMs. Our project page is available at https://wjdghks950.github.io/mol.github.io/.

Ancient script image restoration is a fundamental problem in computer vision, as it directly affects the reliable analysis and interpretation of historical documents and inscriptions. Ashokan Brahmi is an ancient script extensively used during the reign of Emperor Ashoka in the 3rd century BC, primarily for inscriptions in Prakrit. These inscriptions, including major and minor rock and pillar edicts, constitute a valuable yet largely unexplored source of data for computational analysis. The degraded nature of inscription imagery and the lack of standardized digital resources pose significant challenges for automated processing. We present an end-to-end AI-based framework for understanding ancient inscriptions that encompasses image enhancement, optical character recognition (OCR), transliteration, and neural machine translation (NMT). The proposed pipeline processes low-quality images captured directly from stone inscriptions, performs image restoration and Brahmi script character recognition, maps the recognized characters to the Roman script, and finally translates the resulting Prakrit text into English. We also introduce two new datasets: (i) InscriptionOCR Dataset: the largest publicly usable digital OCR dataset for Brahmi script to date, consisting of over 200,000 character images across about 600 classes, and (ii) a bilingual Prakrit-English parallel corpus comprising over 2,000 sentence pairs for NMT. We believe that the proposed framework and datasets will facilitate future research in ancient script analysis, low-resource OCR, and digital epigraphy.

Crowd simulation plays a central role in robot navigation, autonomous driving, and urban planning. For these applications, realistic simulation requires crowds to adapt their behavior to environmental changes and user objectives. However, existing methods that rely on predefined control settings have limited flexibility in accommodating new user-specified objectives. To address this limitation, we propose Ctrl-CWM, a multi-agent Controllable Crowd World Model that integrates crowd generation and run-time control. Our key idea is to adapt the world-model principle of planning using imagined futures to crowd simulation. To this end, Ctrl-CWM consists of an encoder that learns a representation of human motion dynamics, an actor that proposes pedestrian displacements, a critic that evaluates imagined crowd trajectories, and a planner that selects actions. We first learn human motion dynamics through trajectory prediction on real-world pedestrian videos and then freeze the encoder to preserve them. Using this representation, the actor generates imagined crowd trajectories through repeated state updates, and the planner combines the critic's scores with user costs to select actions. Repeated planning advances the simulated crowd, while additional user costs introduce new control objectives without retraining. We extensively evaluate crowd generation under varied agent arrival conditions and run-time control across avoidance and attraction scenarios. Ctrl-CWM outperforms the state-of-the-art method on most crowd realism and collision metrics, and adapts crowd behaviors to user-specified objectives introduced during simulation. The project page is available at https://jungyu0413.github.io/Ctrl-CWM

In this paper, we prove that $\mathbb{Q}$-Gorenstein projective complex varieties admitting int-amplified endomorphisms are of Calabi–Yau type.

We investigate the semiclassical Einstein equation for a quantized scalar field in four-dimensional anti-de Sitter (AdS) and de Sitter (dS) spacetimes. We first determine self-consistent configurations by fixing the bare cosmological constant to its geometric value, requiring the renormalized vacuum stress-energy tensor to vanish. In AdS, the resulting mass-curvature relations depend on the curvature coupling and boundary conditions; one formal Neumann root for minimal coupling is excluded by the admissible parameter range, whereas both Dirichlet and Neumann solutions are allowed for conformal coupling. In dS, we recover the known self-consistent solution for a minimally coupled massive field. We then evaluate the effective cosmological constant on prescribed backgrounds in four massless configurations. In each case, it takes the form \(\Lambda_{\mathrm{eff}}=A/\ell^2+B/\ell^4\). The competition between classical curvature and vacuum polarization produces a minimum and a zero in the minimally coupled AdS case, while the other configurations are monotonic. Finally, the formal continuation \(\ell\rightarrow i\ell\) fails to reproduce the directly calculated quantum coefficients: their AdS-to-dS ratios are \(29/61\) for minimal coupling and \(-1\) for conformal coupling. These results show that continuation of the curvature scale alone does not establish equivalence between the semiclassical vacuum contributions in AdS and dS.

We report, for the first time, a fully integrated Ho$^{3+}$-doped fluoride glass waveguide laser incorporating a femtosecond laser-inscribed waveguide and waveguide Bragg grating. A line-by-line inscription technique was employed to fabricate the Bragg gratings, yielding highly consistent and reproducible grating characteristics with precise control of the Bragg resonance wavelength. A compact 12.4 mm cavity achieves stable single-frequency lasing at 2062.21 nm with a linewidth of less than 5 MHz. The laser exhibits intrinsically linearly polarized emission. This alignment-free architecture provides a compact and robust platform for integrated mid-infrared single-frequency laser sources.

Pebble games model computations under a fixed space budget. Spooky pebbling allows quantum memory to be released by measurement, with the resulting phases corrected later. We study two-input computations with binary-tree dependencies and determine the optimal work and parallel depth for complete binary trees. Our key idea is to clean up the tree in blocks, reducing repeated recomputation of intermediate values. For the complete tree $B_h$ with $n=2^h-1$ vertices and every space budget $h+1\le s\le n$, we give an algorithm with asymptotically optimal work $\Theta(nh/\log(s+1))$. At the minimum budget $s=h+1$, this improves the $O(n\log n)$ bound of Kornerup, Sadun, and Soloveichik to $\Theta(n\log n/\log\log n)$, resolving their time-optimality question. We also construct a parallel schedule with optimal depth \[ \Theta\!\left(h+\frac ns \max\!\left\{\frac{h}{\log(s+1)},\,1+\log^*h\right\}\right). \] Our lower bounds hold for every full binary tree. We also show that achieving optimal parallel depth can require asymptotically more work than minimizing work alone. Applying our schedule to the RNS point-addition trees in the public implementation of Chevignard, Fouque, and Schrottenloher reduces their Toffoli/AND gate count by $20.86\%$ for a P-224 instance and $22.66\%$ for a P-256 instance, using the same arithmetic circuits and peak workspace.

Thermo-mechanical fracture couples transient heat conduction on a cracked domain with a crack that grows as the temperature and the displacement evolve. Neural energy solvers have been proposed for phase-field fracture and later extended to represent a sharp crack through the network input, but heat conduction on the cracked domain and crack propagation under the resulting thermal stresses have not yet been treated together in these solvers. We present an extended deep energy method for thermo-mechanical crack propagation in which the crack remains a sharp polyline. Two networks represent the temperature and the displacement and receive the crack through a scalar embedding function, discontinuous across the crack and smooth elsewhere, so that both fields can jump across it without a regularization length, and the displacement is enriched near the tip by the Williams expansion with trainable amplitudes. The two fields are obtained by minimizing an incremental conduction functional and the thermoelastic potential energy in a staggered sequence, with Monte Carlo integration on points stratified over background elements, densified near the tip and redrawn during training. The stress intensity factors are extracted by the interaction integral with the area term of Wilson and Yu and checked by a sweep of the contour radius, and the crack advances at the maximum hoop stress angle when the energy release rate of the kink reaches the critical value at the crack-tip temperature. On a stationary thermal edge crack the extracted stress intensity factor agrees with the published value to 0.11%, in a functionally graded shear test initiation agrees with an independent sharp-crack finite element solution to within one load step, and on a notched cruciform specimen the crack paths follow the published solutions under mechanical, thermal and combined loading.

Boson stars are among the best-studied exotic compact objects and constitute one of the few black-hole mimickers for which both the formation mechanism and dynamical behavior can be investigated from first principles. Constructing boson star solutions is generally more challenging than constructing neutron star solutions, often requiring either extremely accurate initial guesses for the oscillation frequency or the use of computationally intensive relaxation methods to solve the field equations. In the strong-coupling limit, massive boson stars can be described effectively as perfect- fluid configurations, enabling their construction using methods analogous to those developed for neutron stars. In this paper, we relax the strong-coupling assumption and derive a phenomenological anisotropic-fluid model for spherically symmetric massive boson stars that remains applicable over a broad range of model parameters. We provide ready-to-use fits for both the anisotropy profile and the effective equation of state in terms of the central scalar-field amplitude and the ratio of the self-interaction coupling constant to the squared scalar-field mass. To validate the model, we compute the masses and radii of boson stars using a standard neutron-star construction approach and compare the results against full boson-star calculations. We find excellent agreement between the two methods, while the new approach reduces the computational cost by a factor of about 10. Our phenomenological fluid framework offers an efficient and accurate method for constructing spherically symmetric massive boson stars and computing their observable properties. We provide a ready-to-use Python implementation of the Tolman-Oppenheimer-Volkoff solver, allowing users to construct boson star configurations within the proposed framework.

Impurity nonequilibrium dynamics in quantum many-body systems is a frontier subject in ultracold-atom physics, which helps uncover microscopic mechanisms of polaron and collective excitation phenomena. Although repulsive interacting systems have been extensively investigated, attractive-interaction dynamics lacks systematic studies owing to intricate couplings among different states. We study a one-dimensional ideal Fermi gas containing an attractive spin-down impurity with initial momentum and analyze time evolution of interspin two-body correlations and impurity momentum. Using exact Bethe ansatz solutions, we simplify correlation matrix elements to finite sums for efficient calculations of eigenstate occupations and long-time dynamical evolution. In the weakly attractive regime, bound-state features appear when the total momentum is below or equal to the Fermi momentum, while mixed oscillatory behaviors arise at larger total momentum. The strongly attractive regime shows locally bound-state dominated dynamics with localized correlation peaks and scattering-induced Friedel-like oscillations. We characterize quantum flutter, the periodic oscillation of impurity momentum, and obtain consistent critical chemical potential values of the impurity via four independent Bethe ansatz approaches. This work clarifies quench dynamics and quantum flutter under attractive interactions, improves the understanding of nonequilibrium quantum many-body properties, and provides theoretical support for relevant ultracold-atom impurity experiments.

Internalizing external skills changes a language agent's capabilities and, with them, the value of its remaining guidance: rules can become redundant, misleading, or insufficient for newly encountered decisions. This creates a coupled problem of learning from skills and adapting the skills that supervise further learning. We introduce SkillCycle, a framework for co-evolving agent policies and skill banks through a feedback loop between skill internalization and rule revision. Our central contribution is to give distillation feedback a second role: token-level contextual differences help locate rules for inspection, while interaction outcomes guide edits to their content and applicability. SkillCycle alternates between two phases: policy learning with a fixed skill bank and router, and rule revision with a frozen policy. Candidate edits undergo rule-level and whole-bank environment comparisons before they guide the next learning cycle. On WebShop, SkillCycle with a 3B model achieves a success rate of 74.74% and a score of 88.37 without inference-time skill inputs, representing relative improvements of 0.73% and 3.96% over the state-of-the-art (SOTA) model, respectively. In Cycle 3 ablations on ALFWorld and WebShop, SkillCycle's no-skill success rates improve by 10.18% and 18.11% relative to a static skill bank, and by 2.41% and 2.50% relative to a single bank update, respectively. These results show that continually revising skill guidance as the agent's capabilities change helps transform external skills into policy capabilities that require no skill inputs at inference. We will release code, configurations, skill banks, and evaluation protocols.

In this paper, we propose a deep learning-based predictive beamforming algorithm for integrated sensing and communications in vehicle-to-infrastructure networks, where echo signals are leveraged to enhance communication performance. We formulate a sum spectral efficiency maximization problem under a sensing signal-to-interference-plus-noise ratio (SINR) constraint and construct a penalty-based unconstrained surrogate objective for network training. Based on this formulation, the beamforming matrix is predicted using sensing echoes and historical beamformers from previous time slots. To this end, we develop a predictive beamforming network that processes sensing echoes and beamforming inputs through separate encoders to preserve their modality-specific characteristics. This separate design enables each modality to learn rich and complementary representations which are more effectively exploited through a cross-attention mechanism compared to naive input fusion. The resulting features are fused via cross-attention, while gated recurrent units capture temporal dependencies across time slots. Simulation results validate the performance of the proposed method.

We formulate a discrete-time leader-defender-attacker game that combines hierarchical interaction within a protective group with competition against an external attacker. The leader seeks to reach a prescribed demand point while avoiding capture, whereas the defender seeks to intercept the attacker while remaining near the leader. To capture their distinct objectives and asymmetric interactions, we introduce a nested equilibrium concept combining a leader-defender Stackelberg relationship with a Nash-type best-response condition for the attacker. For linear dynamics and quadratic objectives, we derive affine response laws and a backward recursion, together with sufficient conditions for unique stagewise solutions. We further express arrival, capture, and interception conditions as quadratic inequalities in the initial joint state, characterizing winning regions under the resulting policy. A receding-horizon algorithm implements the computed control laws using updated state information. Numerical experiments over randomized initial configurations examine the influence of the prediction horizon and compare the proposed method with an independent-control baseline, illustrating differences in game outcomes and the agents' realized costs.

World-Action Models (WAMs) utilize future visual prediction as an intermediate reasoning process to guide action generation. However, existing WAMs typically structure visual imagination according to predefined temporal intervals, without explicitly accounting for the different roles of task-critical interactions and connecting transitions. We argue that effective visual foresight should align directly with task-relevant interactions and their corresponding reasoning demands. To this end, we introduce an event-aligned visual action reasoning framework that organizes visual-action prediction around interaction events. Through event-aligned visual-action supervision, WAM learns to generate event-aligned visual context in each imagined rollout, placing greater emphasis on critical state changes that inform action generation. This shapes the visual reasoning granularity according to the underlying interaction dynamics, with detailed reasoning around task-critical events and coarser progression through connecting transitions. Furthermore, we introduce an execution validity head that identifies the valid portion of each predicted action sequence, avoiding redundant actions during chunked inference. Experiments demonstrate a 10.26 percentage point improvement in DOMINO success rate over baseline and competitive performance on RoboTwin 2.0. It also transfers from DOMINO Level 1 to Levels 2 and 3 without target-level adaptation.

Environments are the foundation of recursive self-improvement: they provide the problems agents work on and the feedback used to evaluate progress. Yet constructing challenging research environments with reliable evaluation still depends on domain experts, limiting their scale and disciplinary coverage. We introduce RSI-Forge, a multi-agent pipeline that turns published papers into executable environments for self-improvement. Three agents coordinate construction, reproduction, and review to produce tasks with automated evaluators; each paper's method is independently reimplemented to establish a baseline score. We present 210 environments across 18 fields, including 90 reviewed by independent human domain experts. Both experts and agent judges give high ratings to the potential for improving the provided starting solutions and the evaluators' ability to distinguish solution quality, whereas experts are more critical of shortcut resistance, faithfulness to the source paper, and whether a single idea can exhaust a task. To validate their use for repeated improvement, we evaluate four models over 3 successive attempts on 120 environments, with each attempt inheriting prior code and notes while model weights remain fixed. At least one model improves after the first attempt in 84% of environments. Models also outperform the reproduced paper methods in 68 of the 120 environments, demonstrating room for gains beyond these baselines. Transcript analysis identifies work beyond parameter tuning in 95% of these successful attempts. Analysis of the resulting trajectories shows that models scoring lower on these tasks explore less, more often accept gains smaller than the reported standard error, and rely more heavily on tuning to the development set. RSI-Forge provides a scalable approach to constructing research environments for training and evaluating self-improving agents.

Several published comparisons of variational quantum optimizers time only runs that reach a target loss, or read the verdict at a single target. Either convention could decide whether an optimizer's costlier steps pay off. We measure how much each convention changes verdicts among Adam, simultaneous perturbation stochastic approximation (SPSA) and quantum natural gradient (QNG), on initializations held out from the selection of settings. We compute the exact metric that preconditions QNG, price every step in circuit evaluations and give every method the same budget. In a median pooled over circuit widths, cost families and a sweep of settings with common misses, SPSA needs more than twice Adam's evaluations to reach a loose target. Dropping the censored runs that miss the target hides this gap. On the global-cost family we hold fixed the settings selected for a strict target. QNG then usually reaches the loose target after Adam but the strict target first. QNG's strict-target lead disappears when the metric's simulator price, linear in the number of parameters, is replaced by an assumed hardware count quadratic in that number. We recommend charging every miss the budget and reporting verdicts across targets.

Deploying Mixture-of-Experts (MoE) models relies heavily on Expert Parallelism, which generates intense inter-GPU communication. Consequently, state-of-the-art inference systems require high-bandwidth, P2P interconnects (e.g., NVLink) in datacenter GPUs to handle massive token routing, making deployment prohibitively expensive. Consumer GPUs offer comparable compute power at significantly lower cost, promising to democratize MoE inference for individuals and enable privacy-preserving local deployments. However, their bandwidth-limited (only weak PCIe bus bandwidth) and host-mediated interconnects (no P2P support) introduce severe communication bottlenecks. We present CoMoE, a communication-efficient MoE inference system that resolves this mismatch through novel host-centric routing. Our key insight is that the unique communication topology provides the opportunity to elevate the host to an active routing hub, which can fundamentally reduce communication volume and eliminate global synchronization-induced stalls. Specifically, for token dispatch, we introduce host-backed token multicast to write shared tokens to the host exactly once, eliminating outbound transmission redundancy. For token combine, we propose a fine-grained, token-level aggregation mechanism using host staging buffers, which replaces rigid global synchronization and mitigates straggler effects. Evaluation on RTX 5090 GPUs shows that CoMoE improves inference throughput by up to 1.46x, approaching the performance of NVLink-capable A800 GPUs at only 23.4% of the hardware cost.

Manifold fitting seeks to recover the geometric structure underlying noisy ambient observations. We propose Successive Tangent Space Projection (STSP), an iterative manifold-fitting method that reduces normal noise while preserving tangential variation. The former improves fitting accuracy, whereas the latter helps retain geometric coverage. We characterise the \rev{nearby population fixed-point set} of STSP as a manifold-fitting object. Under uniform sampling from a compact smooth manifold with positive reach and isotropic Gaussian noise, this set lies within $O(\sigma^2)$ of the underlying manifold, and \rev{nearby population orbits} converge geometrically to it. At the finite-sample level, with high probability, fixed points in the local tube lie within $O(\sigma^2)$ of the underlying manifold up to sampling error, and empirical orbits \rev{initialised within that tube} and generated from a fixed reference sample enter and remain in the same neighbourhood. We further develop a multi-scale extension, MS-STSP, designed to reduce curvature bias while preserving the $O(\sigma^2)$ geometric localization order of STSP at both the population and finite-sample levels. Numerical experiments show that STSP compares favourably with competing methods in balancing fitting accuracy and geometric coverage, and that MS-STSP reduces curvature-induced shrinkage, particularly under high noise.

$\mathbb{Z}_p$-folded surfaces are a class of oriented folded surfaces with a fundamental $H_2(\mathbb{Z}/p\mathbb{Z})$ class. In this paper we study the $\mathbb{Z}_p$-folded surfaces that embed in $3$-manifolds. This perspective naturally leads to the definition of the $\mathbb{Z}_p$-Thurston norm, which generalises the $\mathbb{Z}_2$-Thurston norm of Jaco, Rubinstein and Tillmann and adapts Turaev's definition of $\theta$. We define canonical $\mathbb{Z}_p$-folded surfaces, which connect the theory of $\mathbb{Z}_p$-folded surfaces to the study of one-vertex $3$-manifold triangulations, and we relate their Euler characteristic to the $\mathbb{Z}_p$-Thurston norm. We generalise a classical result of Bredon and Wood by proving that the maximum Euler characteristic of a non-separating non-empty $\mathbb{Z}_3$-folded surface embedded in $L(3n,1)$ is $2-n$ for $n\in\mathbb{Z}^{>0}$, determining the $\mathbb{Z}_3$-Thurston norm in these cases. We conclude by demonstrating the motivating application of this theory to the study of generalised triangulations by proving that any generalised triangulation of the lens space $L(3n,1)$ must have at least $n$ tetrahedra. This final result is a preview of joint work with Spreer in which we determine the exact complexity of $L(3n,1)$ using more sophisticated techniques.

Rydberg-atom quantum uniform linear arrays (RAQ-ULAs) offer a promising sensing architecture for direction-of-arrival (DOA) estimation in terahertz (THz) beam alignment. Existing studies often model the quantum receiver as a macroscopic linear block and rely on the Cramer-Rao bound (CRB) for array evaluation or power allocation. However, as a local variance bound, the CRB cannot capture threshold breakdown caused by spatial ambiguities in low-signal-to-noise-ratio (SNR) regimes. This paper proposes a physics-aware power optimization framework for RAQ-ULAs based on stochastic Barankin bound minimization. We derive a closed-form stochastic multipoint Barankin bound (BRB) matrix under a low-SNR integrability condition and introduce an arcsine-prior calibration to characterize bounded-domain error saturation. By incorporating a Lindblad-guided electromagnetically induced transparency (EIT) readout model, we couple the ambiguity-sensitive BRB with photon shot noise, power broadening, and laser Rabi frequencies. A CRB-optimized analytical baseline is further derived to expose the limitation of local-SNR-based allocation. To solve the resulting nonconvex problem, we develop a backtracking majorization-minimization (MM) algorithm with a Lipschitz-based quadratic surrogate. The algorithm ensures monotonic decrease and converges to a feasible stationary point. Simulations show that the proposed framework predicts threshold breakdown more accurately than the CRB and enlarges the reliable operating region under severe THz attenuation.

Cancer is driven by an estimated two to nine gene mutations, known as multi-hit combinations. Due to the large number of genes, identifying these multi-hit combinations presents a computationally challenging problem, which has previously required supercomputers to enumerate all or most gene combinations. Recent work formulated this classification task as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP) and solved it via column generation on a single commodity CPU, where a pricing problem identifies promising gene combinations (arXiv:2602.22551). The main bottleneck is the pricing problem that has to be solved repeatedly. To solve the pricing problem to optimality, we propose a dedicated depth first search method that enumerates all possible gene combinations. Although enumerating gene combinations with depth first search have been performed on supercomputers with around 150,000 CPU cores (arXiv:2603.16721), our depth first search algorithm solves the pricing problem to optimality within seconds on a single CPU by leveraging dual information to prune large parts of the search space. By eliminating this bottleneck, our approach yields the first exact method for the MHCDSCP, which is guaranteed to find a global optimal solution.

Let $X$ be a complex $\mathbb Q$-factorial Gorenstein Fano fourfold with $\rho(X)=1$. If $X$ has canonical singularities, we prove that $(-K_X)^4\le3528$, with equality if and only if $(X\simeq \mathbb P(1,1,12,28,42)$. In fact, $(-K_X)^4\ge3130$ already implies this isomorphism. If $X$ has terminal singularities, we prove the sharp bound $(-K_X)^4\le648$, with equality if and only if $X\simeq \mathbb P(1,1,1,1,2)$. In the canonical case, we also obtain the sharp bound $(-K_X)^4\le1024$ when a positive generator of $Cl(X)/ \mathrm{tors}$ is Cartier outside a finite set. The proofs use jet estimates involving all Harder–Narasimhan slopes of the tangent sheaf, the geometry of algebraic foliations, and the integrality of intersection numbers on a general leaf. The equality case in the canonical bound is determined by two computations of divisorial section rings.

Pointing-gesture visual grounding requires connecting hand geometry with the visual identity and extent of a referred object. A central challenge for continuous latent reasoning is how to organize these complementary cues into useful intermediate supervision. We propose Spatial Latent Reasoning (SLR), a framework that structures this supervision around an ordered sequence of geometric and visual states. A spatial ray state is supervised by fingertip position and pointing direction, followed by four states aligned with target-region features. To construct the visual targets, we introduce parity pooling, which applies polyphase grouping to average region tokens on four interleaved spatial supports. All states are generated recurrently during training and inference; auxiliary annotations are required only during training. On EgoPoint-Ground, the framework improves mIoU over same-backbone supervised fine-tuning by 2.8, 17.5, and 21.1 percentage points on Qwen3.5-4B, Qwen2.5-VL-7B, and Qwen3-VL-8B, respectively, with improvements on both hard subsets. On YouRefIt, it achieves 77.6% precision at IoU 0.5, a numerical margin of 5.2 percentage points over the reported state of the art under differing evaluation protocols. Ablations support joint geometric and visual supervision on the standard and similar-object sets, and favor parity over three alternative pooling operators on the standard set. These results support task-structured supervision for continuous pointing grounding. We will release the code and supporting materials.

Effective remote monitoring and surveillance using drones are frequently impeded by severe environmental and thermal clutter, dynamic vegetation, target camouflage, and system latency. Drawing inspiration from the hunting strategies of birds of prey that hover and stabilize their vision to isolate subtle ground motion, we introduce trACT (temporal revelation Airborne Camera Trap), a lightweight, real-time aerial robotics framework designed for autonomous consumer drones. The system integrates Temporal Max Pooling (TMP), a low-level signal processing method that transforms imperceptible movement across a rolling integration window into robust value and time encodings, with self-supervised motion anomaly detection to isolate target motion from background environmental motion caused by wind gusts and drone drift. To overcome mechanical and processing delays, trACT combines motion prediction with automated gimbal-stabilized optical zoom verification and equitable multi-target verification balancing. Extensive real-world field experiments in densely forested wildlife habitats and surveillance scenarios demonstrate that trACT successfully bridges the gap between wide-area aerial monitoring and precise, autonomous target verification under challenging operational conditions.

Flow Language Models (FLMs) have emerged as a continuous-state alternative to discrete diffusion language models, yet the role of their continuous representations in reasoning remains unclear. We investigate this question by comparing the reasoning efficiency of FLMs and discrete diffusion models, measured by solution accuracy under matched denoising steps. Unlike discrete diffusion, which passes categorical states between denoising steps, FLMs evolve a continuous sequence representation throughout denoising and decodes it into discrete tokens only at the end. Our theoretical analysis shows, from a superposition perspective, how information retained in these continuous states can benefit reasoning. Intermediate-state interventions provide further empirical support for this theoretical account, showing that removing information about alternative candidates reduces subsequent solution recovery. Together, these findings show that FLMs allow evidence for multiple candidates to persist and inform subsequent reasoning before a discrete answer is produced. Furthermore, our experiments on maze planning and Sudoku tasks show that FLMs achieve greater reasoning efficiency in the few-step regime: FLMs achieves higher sequence accuracy than discrete diffusion baselines at matched model sizes and small denoising steps. On maze planning tasks, FLMs can also achieve comparable accuracy with smaller models. For example, on Maze15, FLM reaches the 95% accuracy target at 64 denoising steps with 36.5% fewer parameters than MDLM. These findings point to continuous state spaces as a promising foundation for reasoning models that require fewer refinement steps.