Papers

The Epoch of Reionization is characterized by the nucleation, expansion, and percolation of ionized bubbles in the intergalactic medium. Interpreting emerging multi-wavelength observations from facilities such as JWST and next-generation 21 cm interferometers requires a detailed theoretical understanding of the 3D morphology of these HII regions and of the residual neutral structures that survive near the end of reionization. We analyze the geometry and physical properties of ionized bubbles and late-time neutral islands in the large-volume 500 Mpc$^3$ radiation-hydrodynamics simulation Lumina. We identify discrete structures with a 3D watershed method and measure their volumes, shape tensors, and internal gas properties. The volume-weighted bubble size distributions evolve substantially across the EoR: characteristic radii shift from Reff~1 cMpc at z>10 to Reff>100 cMpc by z< 6, while watershed-derived sizes exceed line-of-sight mean-free-path measurements by roughly a factor of 3 at intermediate redshifts. The bulk bubble population is predominantly prolate through most of the EoR. By z~6, however, the volume-weighted distribution of the triaxiality parameter T, which distinguishes flattened from elongated structures, becomes bimodal in the fiducial segmentation, with a sharp oblate peak near T~0.25 associated with a small number of very large bubbles during late percolation. The properties of bubble interiors are consistent with inside-out reionization, with median gas overdensities within bubbles decreasing from $\delta$~1 at z=15 toward the cosmic mean by z=6. Beyond a minimum near the resolution scale, the median internal UV radiation energy density increases with bubble size. The residual neutral islands at z< 6 peak in volume-weighted size near Reff~10 cMpc and remain predominantly prolate, consistent with anisotropic residual neutral structure near the end of reionization.

We study finite-time blow-up for a semilinear shifted Tricomi equation with decreasing propagation speed and an oscillatory scale-invariant mass. We focus on the Strauss-type critical regime and prove that every weak solution with finite speed of propagation, arising from nonnegative nontrivial energy data satisfying a suitable localization condition, blows up in finite time. For sufficiently small initial data, we also obtain the corresponding critical exponential upper bound for the lifespan. The proof relies on a positive self-similar solution of the homogeneous adjoint equation represented by the Gauss hypergeometric function. Combined with a previously established lower bound for the nonlinear term and new estimates adapted to the critical case, this construction reduces the PDE problem to a nonlinear differential inequality. An ODE comparison argument then yields both finite-time blow-up and the lifespan estimate.

Social simulation studies how individual behavior and social interaction produce collective outcomes. In social media marketing, campaign actions shape which consumers encounter the content and how they respond; these responses then spread through the population. We propose OranSim, a social simulation framework that connects creative, creator, targeting, and budget choices to this process. Heterogeneous consumers receive exposure according to content matching and platform allocation and generate initial responses, which propagate among 60 population segments. Candidate campaigns share the initial population and aligned random numbers, making their response trajectories comparable under action changes. In a controlled synthetic campaign, doubling the budget approximately doubles reach while lowering mean content match and engagement probability among the reached consumers; mean 14-day cumulative simulated response mass rises to 1.96 times the baseline. LightGBM predictors fitted to 39,000 historical RedNote notes estimate platform engagement with log-scale $R^2$ of 0.56–0.62 in five-fold cross-validation; a separate 12,154-note corpus supplies temporal, unseen-creator, and held-out-niche test splits. Public-data experiments evaluate policy-value estimation and audience ranking, and paired synthetic outcomes test counterfactual scoring. Together, scenario trajectories and engagement estimates support campaign selection according to a prespecified marketing objective. Code is available at https://github.com/OranAi-Ltd/oransim.

This paper presents a hybrid quantum-classical framework for grayscale image compression and decompression, leveraging the strengths of quantum computing and deep learning. The compression pipeline integrates a Variational Quantum Daubechies Wavelet Transform (V-QDWT) and a trainable Quantum Convolutional Neural Network (QCNN) optimized end-to-end to achieve efficient, image-adaptive multi-resolution analysis and entanglement-based feature reduction. Input images are encoded using the Normal Arbitrary Superposition State (NASS) representation, enabling compact and scalable quantum storage. For decompression, we implement inverse QCNN and V-QDWT circuits to reconstruct coarse image features natively, followed by a classical Super-Resolution Generative Adversarial Network (SRGAN) to enhance perceptual quality. Experimental evaluations on benchmark grayscale datasets demonstrate the efficacy of our hybrid approach. By jointly training the quantum layers, the base quantum pipeline closely rivals classical JPEG2000 standards. Subsequent SRGAN refinement substantially pushes the boundaries of the reconstruction, achieving superior structural fidelity (PSNR: 30.0667 dB, SSIM: 0.8744, Histogram Correlation: 0.9244). Histogram analysis and qualitative comparisons further validate the restoration of fine textures and intensity distributions. Our findings highlight the potential of combining variational quantum compression with classical deep learning to enable efficient, scalable, and perceptually-aware image processing in quantum-enhanced computing environments.

Tokenization is a central design choice in genomic language models, yet most deoxyribonucleic acid (DNA) tokenizers use characters, fixed-length k-mers, or frequency-derived subwords without explicitly using prior information about the specificity of DNA-binding regulatory factors. We introduce Motif-Vocab, a biologically informed tokenizer that scans both DNA strands for statistically calibrated motif matches, emits transcription-factor (TF) identity tokens, and applies nucleotide, $k$-mer, or byte-pair encoding (BPE) to unmatched sequence. Motif-specific null distributions put position-weight matrices (PWMs) of different lengths and degeneracy on a common significance scale; deterministic overlap rules make the representation reproducible. In controlled Bidirectional Encoder Representations from Transformers (BERT) pretraining on two billion base pairs, real motif libraries outperform randomized-motif controls on 54 of 55 in-scope downstream tasks. On a motif-disjoint recognition task derived from DART-Eval Task 2, TF-specific tokens improve macro-F1 by 0.040 over a position-matched generic motif token and by 0.033 over a matched no-motif tokenizer (95% bootstrap confidence interval: 0.027–0.038). Motif tokens also receive stronger attribution and produce larger occlusion effects than shuffled controls. Dense no-motif tokenizers remain strong general-purpose baselines, including a near-tie on the five-task BERT-base panel. Thus, Motif-Vocab is not a universal accuracy replacement; it is a targeted, interpretable inductive bias for motif-sensitive genomic modeling.

Reinforcement learning with verifiable rewards (RLVR) supervises mathematical reasoning through final-answer correctness, but provides little guidance on individual tokens. On-policy distillation (OPD) supplies dense feedback on student-generated responses, yet teacher preference need not reflect correctness. Recent hybrids combine OPD and verifier-derived advantages or reweight task credit using teacher ratios. However, teacher guidance enters after verifier-based group normalization, and token reweighting need not preserve the total task credit assigned to each response. We introduce Unified Entropy-Calibrated Credit Redistribution for GRPO (UECR-GRPO), which integrates verifier and teacher signals within a single GRPO-style update at both the response and token levels. Path-Utility Unification (PUU) combines verifier reward and a teacher-to-anchor path log-ratio in a single KL-regularized objective. Its on-policy implementation uses a length-normalized teacher score and combines both rewards before group normalization and PPO clipping, allowing teacher evidence to influence the response ranking. Entropy-Calibrated Redistribution (ECR) then uses the signed teacher–old-policy token gap to redistribute the verifier-derived component. Full-vocabulary teacher entropy attenuates uncertain guidance, while a response-wise zero-sum projection preserves the total task credit and its token-wise sign before clipping. Across five mathematical reasoning benchmarks, UECR-GRPO achieves average \(\mathrm{Avg@12}\) accuracies of 17.21% and 65.09% with Qwen3-1.7B and Qwen3-4B students, respectively, exceeding the strongest baseline at each scale by 0.89 and 0.56 percentage points.

Let $A$ be an $\alpha$-Hölder cocycle over a transitive two-sided subshift of finite type, and assume that $A$ is strongly bunched. We prove that if there exist $k\in\{1,\ldots,d-1\}$ and $c>0$ such that \[ \lambda_k(p)-\lambda_{k+1}(p)\ge c \] for every periodic point $p$, then $A$ admits a dominated splitting of index $k$. Thus, under strong bunching, a uniform asymptotic gap in the Lyapunov spectrum of periodic measures implies a uniform geometric splitting along all orbit segments. This extends the periodic-gap criterion of Kassel–Potrie from locally constant cocycles to Hölder cocycles in arbitrary dimension, and extends the two-dimensional fiber-bunched result of Velozo to higher dimensions under the stronger bunching assumption.

Watch time is the primary engagement signal in short video feeds, and its prediction directly affects ranking and exposure. Existing methods improve watch time prediction by correcting duration bias or modeling richer distributions, but most expose only an expected or debiased watch time at serving time. Even when video duration is available to later models, the interface gives only one estimate of watch time and no probabilities for completion, overplay, or other regions relevant to downstream tasks. To address this limitation, we propose the Distributional Serving Interface (DSI), which has a distribution provider, a compact, low-dimensional summary, and lightweight readouts tailored to each task. The provider learns a joint distribution over four watch states derived from watch ratio and their event times; rules based on video duration remove incompatible combinations, while a restoration loss preserves accuracy in seconds. The summary reduces this distribution to a small set of event probabilities, time scales relative to duration, and uncertainty statistics. After training the provider, we fix its parameters and train value and ranking readouts that combine the summary with raw context. Across KuaiRec, KuaiRand-1K, and WeChat21, the complete DSI system achieves the lowest MAE on all three datasets, beating the strongest result among nine baselines by 1.9% to 8.5%, and achieves the best XAUC on two. It also leads retrieval metrics that account for video duration when complete systems are compared. With matched readouts held constant, the summary retains information relevant to each task beyond a predicted mean paired with video duration. Using the same lightweight linear heads for each new target, it also performs best on two new watch-time targets and improves a separately logged engagement target, while a randomly initialized provider does not reproduce this gain.

We investigate how one-loop operator mixing reshapes the flavor sensitivity of lepton-number-violating dimension-7 SMEFT interactions. Using both bottom-up and top-down EFT approaches, we study the interplay of neutrinoless double beta decay ($0\nu\beta\beta$) and neutral current rare meson decays $K\to\pi\nu\nu$, and $B\to K^{(*)}\nu\nu$, which at tree level probe apparently disconnected quark- and lepton-flavor sectors. We show that loop mixing qualitatively changes this picture: flavor structures radiatively feed into one another, substantially extending the sensitivity to higher new-physics scales across operators and flavors. In the bottom-up EFT approach, this can make $0\nu\beta\beta$ highly sensitive even to operators involving heavier-generation quarks, while rare kaon and $B$ decays retain crucial complementary sensitivity to other flavor combinations. A top-down EFT approach example using a ultraviolet model involving scalar-leptoquark illustrates how the same effects can reorder the relative importance of different observables.

Terminal intercept-angle control against a maneuvering target can substantially increase the required missile acceleration, potentially leading to saturation and interception failure unless acceleration limits are explicitly addressed. The engagement is therefore formulated as a linear-quadratic optimal-control problem with bounded acceleration commands. Polynomial approximations of the line-of-sight projection coefficients are used to better represent the nonlinear engagement geometry and estimate the time-to-go. The bounded optimal command is derived over saturated and unsaturated arcs, whose switching times are computed at each guidance step. The guidance law is derived for arbitrary linear missile dynamics and implemented for zero-order missile dynamics. For the zero-order model, the conditions under which the terminal demands can be met are derived in closed form, yielding the minimum and maximum reachable commanded terminal intercept angles. Performance is evaluated in nonlinear simulations. Compared with its unconstrained counterparts, the bounded formulation yields substantially smaller miss distances and terminal-angle errors when saturation is encountered. Unlike corresponding bounded miss-only guidance laws, the proposed law does not reduce to its unconstrained counterpart for minimum-phase missile dynamics because the acceleration command can saturate near the end of challenging engagements. The bounded law anticipates this saturation and compensates through earlier maneuvers.

We prove that the spectrum of a smooth closed three-manifold gives a positive lower bound for the length of its shortest nonconstant closed geodesic. The argument uses three curvature heat coefficients and the first positive singularity of the retarded wave trace. The heat coefficients yield a curvature–length dichotomy: sufficiently large maximum curvature forces a closed geodesic shorter than the curvature scale. We then show that a shortest closed geodesic lying below the conjugate radius produces a singularity of the sine trace. Combining these estimates gives a lower bound depending only on the common spectrum. The compactness theorem of Anderson then implies smooth compactness of the full isospectral family modulo diffeomorphisms.

We investigate the linear growth rate of tearing instability in a resistive force-free current sheet using the linearized fully-compressible magnetohydrodynamics (MHD) equations. Our results show that, as the plasma beta ($\beta$), which is proportional to the ratio of thermal pressure to magnetic pressure, increases, the dispersion relation approaches that of the incompressible tearing mode. As $\beta$ decreases, the growth rate increases but this increase remains finite even in the limit $\beta \rightarrow 0$. The relative increase in the growth rate from $\beta = +\infty$ to $\beta=0$ depends on the Lundquist number, with lower Lundquist numbers showing a more pronounced increase. These findings indicate that, while compressibility has a negligible effect on the growth rate of tearing instability in high Lundquist number regimes, its effect becomes significant at low Lundquist numbers. This suggests that compressibility may influence the critical Lundquist number for the transition from laminar to plasmoid-dominated magnetic reconnection. Moreover, in low-$\beta$ regimes ($\beta < 1$), the generated density perturbation can be substantial, comparable to or even larger than the magnetic field perturbation, even though the growth rate is only slightly modified by the compressibility.

Humanoid control, leveraging human demonstrations, has achieved diverse, agile, and natural locomotion behaviors through reinforcement learning (RL). While this paradigm has yielded remarkable performance in physical humanoid control, how to eliminate specific motions from learned policies remains insufficiently explored. Addressing this issue is motivated by pressing safety and privacy concerns: the removal of malicious, poisoned, or suboptimal motions, as well as copyright-protected motions subject to the right to be forgotten under regulations such as the GDPR, is of critical importance. To this end, we propose {ForgetMimic}, the first motion-level unlearning method designed specifically for physical-world humanoid control. The core idea of ForgetMimic is as follows: given a policy $\pi_\theta$ trained on $N$ motions, our method degrades performance on a target subset of $K$ motions while preserving the effectiveness of the remaining $N-K$ motions. Furthermore, we identify and resolve two key training mechanisms in robot control that lead to unlearning failure. We conduct extensive experiments on the Unitree G1 and H2 humanoid robots across 12 motions, including Dance, Fight, Flip, and others. Experimental results demonstrate that ForgetMimic effectively eliminates memory of designated motions while maintaining the normal operation of all other motions.

Optimization problems (OPs) are key to solving many challenging research problems in robotics. However, reproducibility still remains a major issue. In this paper, we present Amplify, a lightweight nonlinear programming library aimed at reproducible results of robotic-related trajectory optimization problems. The minimalistic requirements for the 537-line library (80 characters per line) are an Internet connection, familiarity with the AMPL modeling language, and a text editor. Our primary contribution is the formulation of a library where trajectory optimization algorithms are represented directly within the optimization model. Specifically, we implement the algorithms used to compute the dynamics, trajectories, and reference motions as constraints of the OP in a declarative programming paradigm. We outline how our formulation of objectives, decisions variables, and constraints can be implemented in other transcription libraries that want to be lightweight and reproducible. We also compare the Amplify framework with 3 other libraries across examples of benchmark optimization problems across several fields, including bipedal locomotion and grasp planning.

In 2006, Katzman showed that the first six Betti numbers of the Stanley–Reisner ring of a flag complex are field independent. He also found flag complexes on eleven vertices whose eighth Betti number depends on the field, and asked whether the seventh is always field independent. We answer this affirmatively by proving a stronger, purely topological result. Let $\tau(d)$ be the least number of vertices of a flag complex whose $d$-th reduced integral homology has torsion. We prove that $\tau(d)\geq d+10$ for every $d\ge0$. This bound yields the field independence of the seventh Betti number. Equivalently, combining our result with Katzman's, for every finite simple graph $G$, the first seven Betti numbers of the edge ideal $I(G)$ are field independent.

Nanowire lasers based on spectrally broad gain materials typically exhibit multimode emission, which limits their utility in applications requiring precisely defined spectral characteristics. In this study, we experimentally demonstrate the selective, narrow-band suppression of individual lasing modes in zinc oxide (ZnO) nanowire lasers through near-field coupling to titania (TiO2) nanopillars. Our study is based on photoluminescence spectroscopy in the lasing regime, which is complemented by finite-difference time-domain simulations. We show suppression of longitudinal nanowire lasing modes by their resonant coupling to the whispering gallery modes in nanopillars of suitable size. In addition to spectral selectivity of the coupling, we reveal two distinct coupling regimes based on polarization matching between whispering gallery modes and nanowire waveguide modes. These findings demonstrate a promising approach towards engineering the spectral emission properties of nanowire lasers through tailored photonic architectures.

A sequence of integers $1=a_0<a_1<\cdots<a_k=n$ is called an addition chain of length $k$ if $a_j=a_s+a_t$ with $0\le s,t<j$ for all integers $j\in \{1,2,\ldots,k\}$. We denote by $\ell(n)$ the minimal length of an addition chain leading to $n$. Here we investigate the distribution of the function $\ell$ through the counting function $$ F(m,r):=\#\{n\in [2^m,2^{m+1}):\ell(n)\le m+r\} $$ and show that, for every fixed $0<c<\log 2$, there exist positive constants $K_1$ and $K_2$ such that $$ K_1^r m^r\le F(m,r)\le K_2^r m^r $$ for all sufficiently large $m$ and all integers $m^{0.9}<r\le cm/\log m$. The upper bound also holds for every integer $r>m^{0.9}$. Moreover, denoting by $G(m,r)$ the number of distinct addition chains of length $m+r$ leading to an integer $n\in [2^m, 2^{m+1})$, we show that there exist positive constants $K_3$ and $K_4$ such that $$ K_3^r \left(\frac{m^2}{r}\right)^r\le G\left(m,r\right)\le K_4^r \left(\frac{m^2}{r} \right)^r $$ provided $m^{0.9}<r<m$. This improves and generalizes previous results on the minimal length of addition chains and addresses a question raised by Paul Erdős.

We prove a multidimensional Birkhoff theorem for a new class of "$C^0$ Lagrangian subsets" in cotangent bundles, obtained as Hausdorff limits of compact exact Lagrangian submanifolds with control on their Liouville primitives. If the successive images of such a subset $L$ under the flow of a Tonelli Hamiltonian admit convergent subsequences in both positive and negative time, then $L$ and all its images are Lipschitz graphs over the base. This extends Birkhoff's celebrated theorem for twist maps of the annulus and its known higher-dimensional generalizations, and provides a first version of such results for merely continuous objects. The proof combines Floer-theoretic graph selectors, variational solutions of the Hamilton-Jacobi equation, and weak KAM theory. We also investigate the rigidity and uniqueness of limiting primitives for this new class of singular Lagrangian subsets, which may be of independent interest in $C^0$ symplectic topology.

Consumers increasingly delegate purchasing decisions to Large Language Models (LLMs) acting as surrogate consumers. Using "Tool-Lab," an adaptation of information-board process tracing that places product attributes behind costly tool calls, we examine how marketing pricing cues (i.e., just-below pricing and promotional framing) influence AI shopping agents. Across eight commercially deployed LLMs from three providers, we trace pre-choice information acquisition. Under zero cost, pricing cues rarely mislead. Imposing acquisition costs under a vague goal prompt leads LLMs to omit diagnostic attributes required to compute unit price and choose suboptimal choices resembling human heuristics. Relative to a specific goal prompt that mainly preserves diagnostic search and choice optimality, a vague goal prompt under constraints creates a search-mediated vulnerability. This research demonstrates that marketing heuristics in delegated AI shopping are governed by storefront information architecture, not necessarily immutable LLM flaws.

Generalized Langevin equations describe non-Markovian dynamics in which the evolution of resolved variables depends on their past. We propose a memory-conditioned diffusion method for learning stochastic flow maps of these dynamics from observed trajectories, without identifying a memory kernel or reconstructing unresolved variables. A compact, recursively updated bank of exponential filters enables the flow map to retain predictive history over multiple time scales without conditioning on long observation windows. The next-step distribution is conditioned on the current observation and this memory state, whose storage and update costs are independent of the history length for a fixed bank size. Predictive criteria guide the memory budget, with reference-assisted selection in the vector benchmark, and an optional linear projection further reduces the conditioning dimension. A kernel-based score estimator generates conditional samples without training a score network, and these samples are used to train a neural flow map for autoregressive simulation. Three numerical examples assess long-memory retention at small conditioning dimension, predictive compression in coupled vector dynamics, and non-Gaussian conditional distributions and intermittent events. The non-Gaussian example reproduces conditional asymmetry and burst statistics in a stochastic model of the plasma scrape-off layer.

While the Jacobian of a planar harmonic mapping keeps a constant sign, the signed and the unsigned area elements agree up to that sign, and the two natural moment hierarchies coincide. Once the Jacobian changes sign the critical circle acquires a caustic as its image, part of the plane is covered several times with opposite orientations, and the hierarchies part company: integrating a radial weight against $J_F$ lets overlapping sheets cancel, giving the degree-weighted moments $J_n$, while integrating against $|J_F|$ lets every sheet count positively, giving the multiplicity-weighted moments $J_n^{\pm}$. These are the classical degree and area formulas for the same map, the second weighted by the multiplicity function (Banach indicatrix). It is the second family, the one the caustic threatens, for which a closed form is no longer automatic. For the two-monomial map $F(w)=w+iC\bar w^{k}$ on an annulus we show that it has one anyway: $J_n^{\pm}$ is the total variation of the very same explicit primitive whose endpoint difference gives $J_n$. Crossing the caustic therefore costs exactly one extra evaluation point, the critical radius $r_*=(k|C|)^{-1/(k-1)}$, and it is the same point for every order $n$: the weight $|F|^{2n}$ is nonnegative and so contributes no sign change of its own. On the degree-weighted side $J_n$ has a boundary-only closed form for every $n\ge0$, the zeroth being the signed area of the image counted with degree, and the complex-weighted moments vanish unless $(k+1)\mid(m-\ell)$. Neither weighted integral is a new object, and the caustic of this family has been located before in the literature on harmonic trinomials; what is new is the closed evaluation of the multiplicity-weighted hierarchy across it.

Simulations of electrochemical materials and systems accelerate technological progress, but are still limited by computational power. In particular, quantum computing offers prospects for higher resolutions, due to the exponential amount of data that can be stored in a quantum state. As current quantum computers are still noisy, we consider a hybrid quantum-classical algorithm, that divides the problem into smaller computational tasks. We describe how to implement such an algorithm for non-linear partial differential equations, the Feynman-Kitaev Hamiltonian, in a scalable way for an electrochemical system. We show how it can evaluate general electrochemical models and present a quantum simulation of the Single Particle Model with electrolyte (SPMe) as the first quantum simulation of a battery cell.

We introduce partition functors: algebraic structures indexed by partitions of finite sets and equipped with restriction and transfer maps along refinements. We construct a monad PD on the category of partition functors and on several categories of partition functors with additional multiplicative structure. For a partition ring, exponential elements in its associated completed ring of symmetric functions acquire canonical logarithms after applying PD. This gives rise to a universal exponential relation between multiplicative and additive power operations. For representation rings this can be used to recover the classical relation between symmetric powers and Adams operations, while for Morava E-theory it can be used to recover Ganter's exponential relation between symmetric powers and Hecke operators. We show that the representation rings of products of symmetric groups form the initial partition ring and that, for symmetric monoidal partition functors, the monad PD is closely related to symmetric invariant tensors and the divided power envelope. We also construct a symmetric monoidal partition ring carrying the universal exponential element, so that its image under PD carries the universal exponential relation.

Can entangled noise erase entanglement more efficiently than separable noise? Standard robustness restricts the added noise to separable states; generalized robustness allows any state. We prove that the two costs coincide for every two-qubit state and give an explicit full-rank qubit–qutrit state with a strict gap. Positivity under partial transpose (PPT) characterizes separability in both dimensions, so the boundary is not caused by a failure of the PPT criterion. Instead, product-vector geometry permits a rank-one bridge between the two-qubit dual optimizations and supplies a two-dimensional completely entangled subspace for the qubit–qutrit separation. Local isometric embeddings complete the finite-dimensional bipartite classification, also for any fixed multipartite cut. Combined with known three-qubit separation, the result classifies universal equality relative to full separability in all finite multipartite systems.

Vision-language models (VLMs) offer a promising approach to long-tail autonomous driving, but existing driving datasets provide limited supervision for connecting decision-critical visual evidence with reasoning and planning. We introduce AnchorReasoning, a visually grounded reasoning dataset built on WOD-E2E, containing 416,119 annotated frames and 395,379 decision-critical elements across four major categories and 19 fine-grained types. Each frame is organized as a visually grounded chain-of-thought (VG-CoT) that links decision-critical element identification and localization, element attributes and implications, driving-action rationale, and action and trajectory planning. We further develop a curriculum supervised fine-tuning strategy that progressively learns these hierarchical capabilities, together with an object-size-aware grounding metric for evaluating localization quality. Experiments across eight general-purpose, embodied-AI, and AV-specific backbones show that VG-CoT supervision improves grounded reasoning and trajectory prediction. Across models, 5-s ADE and FDE decrease by 7.84 and 11.86, while RFS Frame and Cluster improve by 1.66 and 1.70. These gains are achieved with 18.5 fewer reasoning tokens and 0.32 s/frame lower inference latency on average, demonstrating the value of visually grounded, decision-focused supervision for VLM reasoning and planning in long-tail autonomous driving.

Given an abelian scheme $A$ over a $p$-adic ring $R$, Borger and Saha constructed a filtered module $\{\mathbf{H}_\delta(A) \supset \mathbf{X}_{\mathrm{prim}}(A)\supset \{0\}\}$ with a semilinear operator $\mathfrak{f}^*$ on $\mathbf{H}_\delta(A)$ using the theory of arithmetic jet spaces. The above object admits a canonical map $\Phi$ to the Hodge sequence $\{\mathbf{H}^1_{\mathrm{dR}}(A) \supset H^0(A,\Omega_A)\supset \{0\}\}$ of $A$ in the category of filtered modules. As a result, by restricting $\Phi$, we obtain a natural $R$-linear map $\Upsilon: \mathbf{X}_{\mathrm{prim}}(A) \rightarrow H^0(A,\Omega_A)$. In this paper, we show that the map $\Upsilon$ is an isomorphism of vector spaces over $K$, the field of fractions of $R$. As a consequence, we will show that for all abelian schemes $A$, the operator $\mathfrak{f}^*$ on $\mathbf{H}_\delta(A)_K$ is a bijection, and our object $\{\mathbf{H}_\delta(A)_K \supset \mathbf{X}_{\mathrm{prim}}(A)_K\supset \{0\}\}$ becomes a filtered isocrystal. In fact, the above results admit a generalization to the setting of semi-abelian schemes. The elements of $\mathbf{X}_{\mathrm{prim}}(A)$ are represented by primitive additive characters of the arithmetic jet spaces attached to $A$. Hence, our isomorphism given by $\Upsilon$ provides an interesting character-theoretic interpretation of $H^0(A,\Omega_A)$ in terms of primitive delta characters. As a result, to any $1$-form $\omega$, the above isomorphism associates a canonical numerical invariant that depends on deformation theoretic data of $A$. Furthermore, we also extend a comparison theorem between $\mathbf{H}_\delta(A)_K$ and the first crystalline cohomology $\mathbf{H}_{\mathrm{cris}}^1(A)_K$ in the general case when the elliptic curve $A$ is defined over the ring of integers of a $p$-adic field $K$ that is a finite extension of $\mathbb{Q}_p$.

Control barrier functions (CBF) are a popular safety filter to ensure safety for nonlinear dynamical systems. However, when the system is subject to uncertainties and disturbances, this requires the use of robust variants of CBFs, which can be difficult to construct and can be overly conservative, especially for high-dimensional systems under input constraints. In this work, we propose a new approach to solve these challenges by introducing Least-Effort Adversarial Potentials (LEAP), a certificate that quantifies the robustness of a given state against disturbances in terms of the effort required by the disturbance to cause failure. We show that LEAP is a CBF for the undisturbed system, but can also be used to construct a safety filter that is robust to disturbances whose cumulative effort is bounded. We propose a method for constructing LEAPs with on-policy deep reinforcement learning. Next, we demonstrate LEAPs in simulation on a variety of multi-agent systems with disturbances and uncertainties. Finally, hardware experiments on a quadruped and quadrotors validate that LEAPs are well suited to tackle the disturbances and uncertainties from real-world robotic systems.

We develop a curvature-domain formulation for continuous-aperture signaling, in which the transmit phase is represented through its second spatial derivative after quotienting out affine piston-and-tilt gauge freedom. The resulting gauge-fixed synthesis operator is bounded and compact, with sharp Poincare-Wirtinger constant $C_L=L^2/\beta_1^2$, and its modal Gram spectrum is available in closed form, $\rho_m=(L/\beta_m)^4$, with $\beta_m$ the roots of $\cos\beta\cosh\beta=1$. Under a bounded-support square-integrable propagation kernel the tangent operator is Hilbert-Schmidt, so the infinite-dimensional capacity is a well-defined Fredholm-determinant supremum. The optimal signaling law is a dual-budget generalized water-filling with one Lagrange multiplier for curvature power and one for phase excursion. From the exact nonlinear phase-only aperture law we derive the coherent tangent channel with an explicit Frechet remainder bound and a multi-chart atlas for large excursions. At the receiver, curvature inferred from noisy phase samples by second differences has a pentadiagonal noise covariance with spectral norm $\Theta(\Delta x^{-4})$. A deterministic diagnostic suite measures each mechanism against its closed form, with a null run beside every claim: the computed spectrum matches $(L/\beta_m)^4$ to relative error $3.78\times10^{-15}$; the tangent remainder has fitted slope 1.0000; the dual-budget law is solved with both multipliers strictly active to a KKT residual of $3.90\times10^{-15}$; the derivative-noise bound is approached to 0.999981; and the differentiation-limited branch is observed at exponent 0.2175, then collapses to 0.0576 once the mode count saturates at the Shannon number, while a flat-propagation null run holds at 0.2019. Curvature is thus a well-posed, gauge-invariant coordinate, and below the Shannon number the gauge, rather than the medium, governs the scaling.

How news media frame and emotionally code a public health emergency shapes public risk perception and trust, yet outbreak-coverage dynamics remain understudied for low- and middle-income countries (LMICs). We examine sentiment and stance in English-language Bangladeshi coverage of the 2026 measles outbreak – the country's most severe in two decades, with over 97,000 suspected cases and 600 deaths across 61 of 64 districts, unfolding after the 2024 change of government and a 2024-2025 vaccine stockout. Using the Internet Archive, we build a reproducible corpus of 403 headlines from seven national outlets (396 in-window in 2026), label them for binary sentiment and four-way stance via a large language model under a locked codebook, and validate against a two-coder human-adjudicated gold standard (n=153; Cohen's kappa=0.89 stance, 0.75 sentiment). Aligned to the DGHS epidemic curve, coverage grew significantly more negative (56% to 88% negative; Cochran-Armitage z=4.12, p<.001) and risk-amplification framing intensified (44% to 84%; z=4.15, p<.001). Media negativity lagged incidence, tracking cumulative mortality. Contrary to the political backdrop, blame remained a minority frame (~9% overall) and was overwhelmingly systemic (32 of 37, 86%) rather than directed at named actors. The pipeline offers a scalable, transparent method for LMIC outbreak-media analysis; Bangladeshi coverage amplified threat far more than it assigned political blame.

Distributed data management systems deployed in untrusted environments rely on Byzantine Fault-Tolerant (BFT) consensus protocols to tolerate malicious failures. DAG-based BFT protocols improve throughput by letting validators disseminate transactions concurrently and by scaling execution across multiple workers. However, imbalances in workload or resource capacity can still degrade performance significantly. This paper presents Flamingo, a load-balancing protocol for certified DAG-based BFT protocols that addresses imbalance at both the ordering and execution layers. At the ordering layer, Flamingo periodically migrates client accounts away from overloaded validators, adapting to skewed submissions and heterogeneous validator capacity while preserving correctness under Byzantine faults, with migrations taking effect only through the committed log. At the execution layer, Flamingo redistributes committed transactions across executor workers using a deterministic, order-preserving scheduler that balances load and minimizes cross-worker data movement, without centralized coordination or costly distributed commit. Built on top of Narwhal and Tusk, our prototype shows that Flamingo recovers throughput and latency under workload skew, validator heterogeneity, and shifting hotspots, adds negligible overhead when the system is balanced, and needs load balancing in both layers, since resolving only one shifts the bottleneck to the other.