Papers

Quadruped robots performing outdoor deliveries must interpret complex scenes, anticipate changes, and navigate in socially compliant ways. Robot demonstrations are costly to collect at the scale needed for generalization. Egocentric web videos offer abundant human navigation experience, but differences in viewpoint and motion make this experience difficult to transfer to robots. We introduce DR-VLA, a Mixture-of-Transformers framework that transfers human navigation experience through a domain-invariant scene representation (DISR). The framework combines vision-language understanding and latent world modeling with a flow-matching action expert. We introduce EgoLynx, comprising 10,000 hours of curated egocentric web video (EgoLynx-Web) and 2,000 clips of teleoperated robot navigation collected during real-world deliveries (EgoLynx-Robot). We pretrain the understanding and world experts on EgoLynx-Web without action labels, then adapt the model to robot observations and train the action expert on EgoLynx-Robot to predict executable trajectories. We also propose the Quadruped Navigation Score (QNS), a pseudo-closed-loop metric combining safety, instruction compliance, comfort, and progress. On the held-out EgoLynx-Robot test split, DR-VLA improves QNS by approximately 5% and reduces open-loop final heading error (FHE) by 14.6%, each relative to the best competing result for that metric. Ablations show that web-video pretraining improves generalization and that the model's key components contribute to performance. As a future-prediction target, DISR outperforms five generic visual representations and yields performance close to task-specific 3D perception without dedicated geometric labels or point clouds for target construction. Trained separately on NAVSIM v1 without web pretraining, DR-VLA achieves 92.1 PDMS, suggesting that the framework also applies to autonomous driving.

Sub-Doppler resonances observed in miniature cells ($V \ll 1 cm^3$) with Rb or Cs atoms in the field of counterpropagating bichromatic laser beams are of interest for the creation of a miniature quantum frequency standard (QFS) of the optical range. However, a theory of these resonances that takes into full account the real structure of energy levels in an atom has not yet been constructed, which would make it possible to obtain explicit analytical expressions for the absorption coefficient of the medium. This paper addresses this gap using the density matrix formalism and the algebra of irreducible tensor operators. Namely, we obtained an analytical expression for the absorption coefficient of the probe beam in the presence of a more intense counterpropagating beam (pump-probe regime). Moreover, the calculations were carried out for arbitrary parameters of laser beam polarization, arbitrary angular momenta of optical dipole transitions in the atom and various relaxation processes. The constructed theory allows us to correctly take into account the simultaneous action of various nonlinear optical effects, in contrast to the simplified three-level model of the atom, and also to investigate the partial contribution of each of them to the overall observed resonant circuit. The analysis performed, in particular, made it possible to predict an increase in the amplitude of the sub-Doppler resonance when using counterpropagating light beams with opposite circular polarizations in relation to the configuration of counterpropagating beams with orthogonal linear polarizations, which is often used in practice.

In 1984, Bressoud and Subbarao established an interesting weighted partition identity connecting the partition function and the divisor function. Recently, the first author, jointly with Bhoria, Eyyunni, and Maji, extended the work of Bressoud and Subbarao and obtained the following analogous weighted partition identity. For any $n \in \mathbb{N}$, they obtained \begin{equation*} p^{(2)}(n) = \sum_{\pi \in \mathcal{D}(n)} (-1)^{ \# (\pi) }s(\pi) \left( \ell(\pi) - s(\pi) \right). \end{equation*} In the present paper, we provide a combinatorial proof of the above identity and extend the result for $p^{(k)}(n)$, where $p^{(k)}(n)$ denotes the number of partitions of $n$ into exactly $k$ distinct part sizes.

This paper proposes a Projection Anderson Acceleration (PAA) algorithm for variational inequality (VI) problems, where the underlying function is expressed as a finite sum of Hölder continuous functions and satisfies the $\sigma$-star strongly monotone condition that includes the star strong monotonicity with $\sigma = 1$ as a special case. In the absence of quasi-monotonicity and Lipschitz continuity, we establish the evaluation complexity of the PAA algorithm for finding an approximate solution. Specifically, for the star strongly monotone VI problems, the PAA algorithm needs at most $O (\log (\epsilon^{-1}) \epsilon^{2 (\underline{\alpha} - 1)})$ evaluations of the function and projection for finding an $\epsilon$-approximate solution, where $\underline{\alpha} \in (0, 1]$ is the smallest exponent of Hölder continuity of the component functions. We illustrate our theoretical results by numerical examples of non-quasi-monotone complementarity problems and non-monotone semilinear elliptic equations with non-Lipschitz terms.

Multimodal large language models (MLLMs) have demonstrated promising capabilities for remote sensing reasoning, yet they frequently generate visually unsupported reasoning that contradicts the visual evidence. Existing post-training methods optimize primarily for final-answer correctness, providing limited supervision for identifying and correcting hallucinations that arise during the reasoning process. To address this limitation, we propose FaithRS, a hallucination-aware self-reflection framework for faithful reasoning in remote sensing. We first construct SFHD-43K, a dataset of 43K structured, fine-grained hallucination annotations, and train a detector to identify hallucination types, underlying causes, and supporting visual evidence. FaithRS then incorporates this diagnostic feedback into a Safe Detector-Guided Corrective Rollout framework, where a safety-aware gate selectively determines whether and how to revise the response. Training is driven by a composite reward that jointly optimizes answer accuracy, reasoning faithfulness, hallucination reduction, format compliance, and revision safety. Experiments with Qwen3.5 backbones (0.8B, 4B, and 9B) show consistent improvements across four remote sensing benchmarks, with gains of up to 11.64 points.

Recent exoplanet surveys reveal a systematic trend in the mass ratios of giant planet pairs ($> 30 M_\oplus$). Although the $M_{outer}/M_{inner}$ is broadly centered near unity, it exhibits a dependence on orbital separation. Compact pairs tend to have comparable masses, whereas widely separated pairs show outer-heavy configurations. To investigate the origin of this trend, we perform two-dimensional hydrodynamic simulations that couple gas accretion and orbital migration of two giant planet embryos with initial masses of $15-30 M_\oplus$. We explore the effects of disk viscosity, surface density slope, and initial mass ratio on the coupled evolution of planetary growth and migration. We find that convergent migration drives the planets to open a common gap, restructuring the gas flow. This configuration induces asymmetric accretion, in which the inner planet becomes starved as gap clearing suppresses its gas supply, while the outer planet continues to accrete from the high-density region at the outer gap edge. Consequently, the system naturally evolves toward mass-ratio convergence, and in many cases produces an inversion of the initial core-mass hierarchy. We further show that migration outcomes are highly sensitive to initial conditions. Systems with initially more massive inner cores tend to diverge, whereas steeper surface density profiles and more massive outer cores favor convergent migration and subsequent resonance capture. Overall, our results identify common-gap-driven asymmetric accretion as a unified mechanism linking orbital architecture, resonant capture, and the observed mass-ratio demographics of giant planet pairs.

This work studies the linearization of Ruggeri's classical symmetric hyperbolic model of viscous, heat-conductive fluids about a homogeneous equilibrium. In three space dimensions, we show that perturbations in $L^1\cap L^2$ decay in $L^2$ at the rate $(1+t)^{-3/4}$, uniformly as a common parameter scaling the three relaxation times tends to zero. The estimate controls the equilibrium variables together with the appropriately weighted stresses and heat flux, and has the same decay rate as the formal Navier–Stokes–Fourier limit.

Privacy Support Tools (PSTs) help users control their digital data, but face low adoption due to resignation and overwhelm. While current regulations aim to enhance privacy control, users still struggle to manage their privacy. To address this, we explore how PSTs can be designed for long-term adoption by applying the theoretical lens of psychological needs, as their fulfillment motivates users to use a digital product. We conducted in-depth interviews with 15 users and identified Security, Autonomy, and Competence as key psychological needs. From our results, we derive implications and recommendations for the need-sensitive design of PSTs.

Polynomial excitations consisting of creation and annihilation operators are studied. Subsystem entanglement is proven produced and preserved by such manipulations. NPT entanglement already present between any two subsystems of a general pure or mixed multipartite Gaussian state is preserved under all polynomial excitations. Nevertheless, these excitations can create NPT entanglement between initially separable subsystems, implying that the number of NPT entangled pairs cannot decrease. Polynomial excitations of a wide class of initially separable pure states are considered. For these states, the method reduces the infinite-dimensional positivity problem to a finite-dimensional one: after partial transposition, NPT entanglement is equivalent to a corresponding bilinear representation matrix not being positive semi-definite. Furthermore, using symplectic diagonalization and spectral decomposition, an explicit transformation is constructed between the Fock-space and position representations. It is applied to quadratic excitations of a three-mode mixed Gaussian state. The behavior of the NPT entanglement is tracked between subsystems as a function of a parameter $\kappa$, which tunes the non-locality of the excitation, and quantum negativity is evaluated. Under a chosen quadratic Hamiltonian, the resulting unitary time evolution maintains NPT entanglement for long intervals, interrupted only by short periods of PPT states. Finally, a closed analytical expression is derived for the covariance matrix of a general quadratic operator for an arbitrary number of degrees of freedom in phase space. Our framework directly connects mathematical foundations, theoretical modeling, and experimentally feasible implementations.

In this paper, we prove a uniform pseudolocality theorem for smooth complete Ricci flows whose initial metrics have Ricci curvature bounded below and uniformly positive injectivity radius. No a priori curvature bound is assumed on the flow. As a consequence, we obtain strong uniqueness for smooth complete Ricci flows from a complete metric with the above geometric bounds. We also prove that every smooth complete Ricci flow from a complete Ricci-flat metric with uniformly positive injectivity radius is stationary. The same conclusion holds for any complete flat initial metric. In particular, we give an affirmative answer to Chen's question on the strong uniqueness of Ricci flow from Euclidean space in every dimension.

In this work, we present a fundamentally new approach to visual servoing using lines. It is based on a theoretical and geometrical study of the main line representations which allowed us to define a new representation, the so-called binormalized Plucker coordinates. They are particularly well suited to visual servoing. Indeed, they allow the definition of a proper image line alignment concept. The control law which realizes such an alignment has moreover several properties: partial decoupling between rotation and translation, analytical inversion of the motion equations and global asymptotic stability conditions. This control law was validated both in simulation and experimentally in the specific case of an orthogonal trihedron.

Variance squeezing of a V-type atom interacting with a dissipative cavity is investigated. First, the influence of atomic initial state parameters on the variance squeezing is explored. The results show that the atomic variance squeezing switches alternately between Sx and Sy as the initial state parameter alpha sweeps from -pi to pi. The two squeezing intervals are symmetric about alpha = pi/4, each with a width of pi/2. For alpha = pi/14, only the Sx component can generate variance squeezing and will eventually disappear with time evolution due to unavoidable environmental noise. Then, the influence of system parameters on the variance squeezing is also studied. It is found that, the optical variance squeezing depth of Sx is determined solely by the atomic initial parameters and is independent of the system parameters. Both weak cavity-environment coupling and atom-cavity detuning can significantly enhance the robustness of the Sx variance squeezing. The SGI parameter has an extremely weak influence on variance squeezing. These results are beneficial for high-precision quantum communication applications.

Real-time control systems may experience sporadic computational overloads that cause controller executions to overrun their expected deadlines, affecting the timely update of control inputs. Such overruns are classically handled with static decisions, e.g., by either stopping and discarding the late execution at the deadline instant, or continuing it while skipping the next activations. This paper first demonstrates that such static policies can lead to suboptimal performance when the controlled system undergoes varying operating conditions, and thus proposes a control-driven hybrid overrun strategy that optimally adapts the deadline miss handling at runtime. We model the closed loop as a Markov jump linear system, whose modes encode overrun histories, and we formulate a scenario-tree-based stochastic model predictive control problem that predicts and optimizes over possible sequences of deadline hits and misses. We evaluate our proposal on linear benchmarks including a double integrator and an aircraft pitch system.

The goal of this note is to provide a human written exposition of OpenAI's recent proof that Thompson's group F is nonamenable.

Multi-bit watermarking embeds a message, typically an account identifier, into LLM output so that harmful text can be traced to its origin. We show an attack technique that allows to alter the watermarking message. This allows to, for example, exchange the embedded account ID to an arbitrary different one. The attacker mainly needs access to a few accounts for generating LLM output and model logits, but crucially not the secret key used to watermark. The attacker then rewrites the text, keeping its meaning, so that the watermarking message decoder recovers the watermarking message embedded by the attacker. We are, to our knowledge, the first to propose such an attack, which we call a targeted displacement. Theoretically, we present upper and lower bounds on the probability of our attack succeeding. This bound depends on the number of accounts the attacker has access to, the length of the message and some characteristics of the given text. Our attack can succeed whenever we can bound the ambiguity of the generated text well enough. Empirically, we test our attack technique against five watermarking methods and four LLMs. Attack success tracks our predicted bounds, allowing us to alter watermarking messages in almost all cases with high accuracy, given enough accounts. Our code can be found at https://github.com/Batorskq/PinIt.

This paper investigates the 2D quasilinear wave equation $\displaystyle\sum_{\alpha,\beta=0}^{2}g^{\alpha\beta}(\partial\phi)\partial_{\alpha\beta}^{2}\phi=0$ with the short pulse initial data $(\phi, \partial_t\phi)|_{t=1}=(\delta^{2-\varepsilon_0}\phi_0(\frac{r-1}{\delta},\omega), \delta^{1-\varepsilon_0}\phi_1(\frac{r-1}{\delta},\omega))$, where $0<\varepsilon_0<1$ is a fixed constant and $\delta>0$ is a small parameter. In our previous work [Ding Bingbing, Xin Zhouping, Yin Huicheng, Sci. China Math., Vol. 69 (2026), No. 3, 667-736], we have established the global existence of a smooth solution $\phi$ under the $k$-th order null condition ($k\ge 2$) when the $(k+1)$-th order null condition fails, provided that $0<\varepsilon_0<\varepsilon_k^*=\frac{k}{k+1}$. As a natural continuation, the present paper demonstrates that for $\varepsilon_0\ge \varepsilon_k^*$, the smooth solution $\phi$ blows up in finite time. Consequently, the threshold $\varepsilon_0=\varepsilon_k^*$ is shown to be the critical exponent that precisely characterizes the global existence and finite-time blowup for smooth short pulse solutions to the aforementioned 2D quasilinear wave equation, under the assumption that the $k$-th order null condition holds while the $(k+1)$-th order null condition does not. A key novelty of our approach lies in deriving sharp orders of $\delta$ for almost all quantities in both energy and pointwise estimates. This is achieved by utilizing the higher-order null structure in conjunction with a new good unknown recently introduced by us and the transport equation for the difference between this good unknown and its corrector.

Living supramolecular materials such as microtubules and actin filaments assemble and function in dynamic, heterogeneous environments, subject to chemical concentration gradients. Their rapid and precise response to such gradients—via aggregation, disassembly, or autonomous motion—underlies the fine spatiotemporal control typical of living systems. Reproducing such responsiveness in synthetic materials is a central challenge in materials science and requires a molecular-level understanding of how gradients couple to supramolecular structure and dynamics, which remains difficult to access experimentally. To this end, we combine implicit-solvent coarse-grained molecular dynamics (MD) with the constant chemical potential MD (C${\mu}$MD) technique to investigate, at molecular resolution, the coupling of two prototypical supramolecular polymer models with externally imposed ionic concentration gradients. Despite their contrasting responses to homogeneous ionic conditions, both systems undergo pronounced spatial reorganization under the gradient, generating regions of locally enhanced supramolecular activity that are inaccessible to homogeneous systems with the same overall content of self-assembling species. Crucially, the local supramolecular dynamics is largely determined by the local concentrations, consistent with the formation of local quasi-equilibria: this direct connection between spatial composition and supramolecular activity emerges as a common governing principle across the two models. These findings shed light on the spatially complex supramolecular response that can be triggered by chemical gradients, and show how a single gradient simulation can encode this response across a continuous range of local chemical environments, thus providing a general strategy to investigate and design materials operating under spatially heterogeneous conditions.

City-scale 3D grounding is commonly formulated as candidate ranking, which requires precomputed instance proposals and becomes inefficient in large outdoor scenes. We propose Urbex, an agentic vision-language framework that instead casts grounding as active spatial search. Urbex represents a city-scale 3D scene as an interactive multi-view environment, allowing a VLM agent to query landmarks, zoom into local regions, render oblique views, and commit a grounded bounding box. We optimize this tool-use policy with reinforcement learning on CityRefer, using smooth localization rewards and lightweight shaping rewards for efficient exploration. Experiments show that Urbex achieves the best Hit@1 and IoU on CityRefer, supports candidate-free grounding without ground-truth boxes, and is substantially faster than the strongest city-scale ranking baseline. Zero-shot results on STPLS3D-Refer further indicate improved cross-scene robustness.

We introduce ABot Embodied Reasoning (ABot-ER), a unified embodied reasoning foundation model that breaks the tension between breadth and depth in embodied reasoning. Embodied intelligence demands the joint mastery of perception, planning, and execution, yet reconciling generality with specialization across this spectrum remains an open challenge. Within a single unified model, ABot-ER commands specialist-level depth across all three competencies, spanning spatial, scene, and temporal reasoning in perception; long-horizon action organization in planning; and point grounding and affordance in execution. The Agentic Data-Model Self-Evolution Engine continuously adapts data strategies to the model's evolving capability state. The Task-Conditioned Adaptive Training Strategy uses task tokens to activate lightweight low-rank residuals over a shared backbone, separating updates from heterogeneous output formats while retaining shared embodied knowledge. Across a systematic evaluation on twelve benchmarks covering three core competencies and five capability dimensions, ABot-ER achieves state-of-the-art overall performance across perception, planning, and execution within a unified parametric framework, demonstrating that breadth and depth can coexist in unified embodied reasoning.

Game-theoretic benchmarks claim that large language model (LLM) strategic decision-making varies across game types, interaction structures, and capability dimensions. However, they only evaluate strategic performance across individual fixed models. In parallel, contemporary LLM routers pick models under quality-cost trade-offs, but with no notion of a strategic structure. They do not account for an opponent that might be unknown, and that can adapt over time and shift the feedback signal. To address this, we extend the game-theoretic evaluations and define strategic selection as the meta game layered on top of the base game. In each round, a strategic selector fields an LLM from a portfolio of models to navigate a game payoff matrix that is latent and learned online. We find that the evaluation signal is game-specific, and that extracting a reliable signal requires a much higher number of seed runs $N$ compared to traditional benchmarking setups. Evaluating across 5 games and 10 LLMs, we show a model's strategic competence varies significantly depending on the game setup and the opponent faced. Building on this, we implement a suite of selector methods and find that approaches that rely on query embeddings or LLM self-reflection do not consistently capture the underlying strategic signal. A lightweight multi-armed bandit algorithm performs more reliably across games, though it still falls short of the best fixed model. Finally, we show that simple non-stationary and adversarial bandit variants fail to outperform a stationary bandit baseline, pointing to a gap in how current methods handle a shifting opponent in strategic settings.

It is shown that the random prime Dirichlet series $ X(s)=\sum_{p\in \mathcal{P}}\frac{\xi_p}{p^{s+1/2}} $ can be almost surely approximated by a Brownian motion, where $ \{\xi_p\}_{p\ge 1} $ are independent and identically distributed random variables with zero mean and finite variance, and $ \mathcal{P} $ is the set of prime numbers. As a consequence, the functional law of the iterated logarithm, limit laws of the iterated logarithm, and Chung's law of the iterated logarithm for $ X(s) $ are obtained. It is also shown that the random Dirichlet series $ Y(s)=\sum_{k=2}^{\infty} \frac{(\log k)^{\alpha}}{k^{s+1/2}} $ with $ \alpha=-1/2 $ admits the same approximation as $ X(s) $, and a direct relationship between $ X(s) $ and $ Y(s) $ with $ \alpha=-1/2 $ is established. The strong invariance principle for $ Y(s) $ with $ \alpha>-1/2 $ is also obtained.

A robot following a multi-step instruction needs to act on the right objects in the right order, even as the scene changes. It must also maintain awareness of task progress and determine when to advance. To address these challenges, we introduce Orchestra, an agent harness that separates task planning and execution management from action generation. Orchestra decomposes a complete multimodal instruction into ordered subtasks, tracks completed steps, and updates the locations of relevant objects and destinations during execution. It maintains a shared context containing the active subtask, spatial grounding, and recent observations. An action policy uses this context to generate actions, while a separately trained progress evaluator estimates when to advance to the next subtask. To evaluate whether robots trained on atomic instructions and short trajectories can execute longer subtask sequences, we introduce a benchmark named RMBench-Compose. Orchestra achieves a mean success rate of $68.22\%$ across nine RMBench tasks, outperforming Mem-0 by $26.22$ percentage points. On RMBench-Compose, it achieves an Average Success Length (ASL) of $7.35$ subtasks, $2.46$ times that of HarnessVLA. Across four real-world multi-step tasks, it improves mean ASL by $25.0\%$ over Orchestra using the base $\pi_{0.5}$ policy. These results show that Orchestra helps robots carry out longer sequences of subtasks while preserving the requested subtask order and acting on the specified objects. Our code and project page are available at https://youpengwen.github.io/Orchestra.

We prove that, in every dimension, the relative Euclidean isoperimetric profile of the unit cube equals one whenever the prescribed volume differs from one half by at most $6.25\times10^{-12}$. The only minimizers in this interval are coordinate slabs. This answers Glaudo's question on the existence of a dimension-free central plateau. The proof combines a dimension-free local optimality estimate for slabs, established through BV slicing and a small-support estimate, with a quantitative Gaussian rigidity argument that forces the normal of an approximating half-space to be close to a coordinate direction.

We identify the limit free energy of mean-field multi-species spin glasses with +/-1 spins, allowing for the presence of external fields, and without assuming any convexity property of the covariance function of the Hamiltonian. The limit is given by an "uninverted" variational formula over Brownian martingales. The proof consists in first identifying the limit free energy of configurations with a fixed magnetization. Once the magnetization is fixed, we can show the convergence of the enriched free energy to the solution of a Hamilton-Jacobi equation. The magnetization constraint is also used to show the convexity of the initial condition in this equation, and this yields a variational representation of the solution, as a Hopf formula. Convex duality then turns this formula into an optimization over martingales whose initial values are the prescribed magnetizations.

For a given graph $F$, a graph $G$ is $F$-irregular if all its vertices have pairwise distinct $F$-degrees, where the $F$-degree of a vertex $v$ is the number of subgraphs of $G$ containing $v$ and isomorphic to $F$. While the existence of $F$-irregular graphs has been actively studied for connected graphs $F$, the case where $F$ is disconnected remains entirely unexplored. In this paper, we provide a complete solution to this problem. We prove that for every disconnected graph $F$ with $|E(F)| \ge 2$, there exist infinitely many $F$-irregular graphs. Conversely, if $|E(F)| \le 1$, we show that no non-trivial $F$-irregular graph exists.

Ongoing stage IV galaxy surveys such as DESI or Euclid offer an unprecedented amount of information to study the large-scale structure of the Universe by mapping tens of millions of galaxies. Within the context of cosmic voids, already released and future catalogues will help better understand the void structure and evolution as well as the cosmological model constraints derived from their statistics. With the recent DESI Data Release 1, our aim is to obtain a new void catalogue that allows us to study the properties of cosmic voids at different redshifts, hence providing insight not only on their structure but also on their evolution. We select the DESI BGS and LRG samples for this study. Before the void-finding process, the data goes through a preprocessing pipeline tackling redshift space distortions and reconstructing the mildly non-linear velocity field. After that, the new AVISM void finder is applied to the preprocessed data, obtaining two void catalogues in different redshift bins (0.1 < z < 0.3 and 0.4 < z < 0.8), both within a 1400^3 cMpc^3 cube. We successfully recover N_BGS = 1114 and N_LRG = 216 clean voids with sizes up to ~ 65 cMpc. The void size function, 3D shape variables, density profiles, and linear bias are obtained and analysed. Both the size function and the density profiles obtained are in agreement with previous theoretical studies. The expected mass depletion in void evolution is shown by the evolution of density profiles. We obtain a roughly constant linear bias inside r < Re with mean values of 1.31 +/- 0.02 and 2.14 +/- 0.04 for BGS and LRG, respectively. Both void catalogues are publicly released.

Quantile summaries provide a scalable way to estimate the distribution of individual attributes in large datasets that are often distributed across multiple machines or generated by sensor networks. The state-of-the-art summaries with relative error guarantees of $\pm \varepsilon\cdot \mathrm{rank}$, offering increasingly higher accuracy towards the distribution's tails, are ReqSketch (Cormode et al., JACM 2023) and the recent streaming algorithm by Gribelyuk et al. (SODA 2025). For inputs of size $N$ and probability $\delta$ of exceeding the error bound, ReqSketch achieves space of $O(\varepsilon^{-1}\cdot \log^{1.5}(\varepsilon N)\cdot \sqrt{\log \delta^{-1}})$ memory words, and offers full mergeability, allowing distributed or parallel processing of datasets. In contrast, the latter algorithm exceeds the lower bound of $\Omega(\varepsilon^{-1}\cdot \log(\varepsilon N)\cdot \log\log\delta^{-1})$ from (Cormode & Veselý, PODS 2020) only by a factor of $O(\log\varepsilon^{-1}\cdot (\log \varepsilon^{-1} + \log\log N)\cdot\log^2\log\delta^{-1})$, but it lacks the mergeability property, is substantially more involved than ReqSketch, and has unclear practical performance. Both of these data structures consist of relative compactors from ReqSketch that subsample the stream in a structured way and work well in the streaming setting but are difficult to analyze under mergeability. We design a new relative-error quantile summary that achieves full mergeability and also improves the state-of-the-art streaming space bound to $$O(\varepsilon^{-1}\cdot \log(\varepsilon N) \cdot\log \log \delta^{-1} \cdot (\log \varepsilon^{-1} + \log \log(\varepsilon N) + \log \log \delta^{-1})),$$ which is substantially closer to the lower bound. At the same time, our data structure is simpler than the algorithm from (Gribelyuk et al., SODA 2025) and therefore more suitable for implementation.

The complete intersection forms are the homogeneous polynomials whose annihilator ideal or the Macaulay dual, is an Artinian complete intersection ideal. In this paper, we compute the Waring rank of certain complete intersection forms. As an application, we compute the Waring rank of binomials whose annihilator is a complete intersection ideal. Further, we also compute the Waring rank of the product of binary forms in different sets of variables.

Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.

We take a first step in identifying the superconformal quantum mechanics dual to supersymmetric AdS$_2\times$S$^2$ solutions. We focus on the Type IIB solutions of the form AdS$_2\times$S$^2\times$CY$_2\times\Sigma$ that preserve eight supercharges, with $\Sigma$ a two-dimensional space parametrised by $(x_1,x_2)$, and read off their brane content, a D1-D5-NS5 intersection with D3 and D7 flavour branes. We propose that their dual $\mathcal{N}=4$ quantum mechanics is organised over a two-dimensional lattice of cells in $\Sigma$. Namely, it consists of copies of the linear quiver along $x_1$ dual to the U(1)-invariant solutions of the class, one for each interval along $x_2$, with ranks given by the D1 and D5 charges of the corresponding cell. Its central charge agrees with the holographic one at leading order. We show that the family of SL$(2,\mathbb{R})$ non-Abelian T-duals of the AdS$_3\times$S$^2\times$CY$_2$ solutions of massive Type IIA supergravity, constructed in previous work, belongs to this class, as does the SL$(2,\mathbb{R})\times$SU$(2)$ non-Abelian T-dual of AdS$_3\times$S$^3\times$CY$_2$, and work both out in detail. For both we propose global completions that introduce additional D3 and D7 branes. Along $x_2$ we interpret the fundamental strings stretched between the colour branes and the additional D3 and D7 branes as baryon vertices. Finally, we extend this proposal from the non-Abelian T-duals to the solutions of the class whose defining functions factorise in $x_1$ and $x_2$, including those in which the AdS$_2$ and S$^2$ factors have the same warp factor.