Papers

In this paper, we consider a finite-sum optimization problem, where the objective function is convex, the $n$ component functions are twice continuously differentiable and their Hessians are mean-square Lipschitz. Our contribution is twofold. First, we develop a stochastic algorithm, which requires $\tilde{\mathcal{O}}(n + n^{6/7}/\epsilon^{2/7})$ second-order oracle calls in expectation to find an approximate solution to the problem with the expected accuracy $\epsilon$. Second, we establish a lower complexity bound of $\Omega(n + n^{6/7}/\epsilon^{2/7})$ for any stochastic second-order algorithm satisfying a stochastic second-order version of the first-order linear span assumption, which is widely adopted in the optimization literature. Our lower and upper complexity bounds match up to logarithmic factors and thus resolve an important open question of establishing the optimal complexity of this problem class.

In this note, we extend the matrix-multiplication analysis by OpenAI to rectangular products and prove $\omega(1,k,1)\le2$ for $0\le k\le\frac{1}{2}$, and $\omega(1,k,1)\le1+k+\frac{1}{4k}$ for $k\ge\frac{1}{2}$. In particular, $\omega(1, \frac{1}{2},1)=2$ and the dual exponent satisfies $\alpha\ge\frac{1}{2}$. The proof uses explicit degenerations of convolution tensors, multinomial counting, and Strassen's spectral theorem. An angular constraint on three dot-product parameters gives both the rectangular curve and a bound for $\omega(a,b,c)$. As an application, Zwick's algorithm for all-pairs shortest paths in directed unweighted graphs runs in $O(n^{2.5})$ time. Combining the rectangular bound with the $(\min,+)$-product improvement of Alman and Vassilevska Williams further gives $O(n^{2.4999})$ running time.

We prove that a holomorphic family of connected complex Lie groups has Oka total space if and only if its base is Oka. Extension presentations and generating sections give Oka results for stable and parabolic bundle moduli and for holomorphic mapping and embedding spaces. Every nonempty degree component of maps from a compact Oka curve to projective space is Oka; rational-function spaces are also holomorphically elliptic. For a vector bundle on a smooth projective curve, the Oka property of its nested Quot scheme is equivalent to that of the symmetric powers determined by the length increments. Complete Hamiltonian flows give holomorphic ellipticity of irreducible \(\mathrm{SL}_2\)- and \(\mathrm{GL}_2\)-character and representation loci, for closed surfaces of genus at least two and for surfaces with fixed regular semisimple boundary classes. The Riemann–Hilbert correspondence yields Oka moduli spaces of nonresonant parabolic connections for arbitrary parabolic weights, and holomorphic ellipticity when reducible monodromy is absent. A proper holomorphic fibration over a Riemann surface, with a section and connected complex tori as smooth general fibres, has Oka total space exactly when its base is Oka. For a Schoen fibre product \(X\) of rational elliptic surfaces with disjoint singular values, we construct an entire local biholomorphism \(\mathbb C^3\to X\) whose image contains a dense Zariski-open subset. Further applications treat Hilbert schemes, compactified relative Jacobians, and logarithmic complements.

Quorum sensing (QS) is classically understood as a mechanism by which bacterial cells sense their own density, but environmental fluctuations make any single cell's estimate unreliable. An alternative view holds that populations pool individual estimates to reach reliable collective decisions. We investigate how a two-autoinducer toggle switch network enables this collective adaptation in fluctuating environments. At the single-cell level, the toggle switch is bistable. Membrane permeability controls autoinducer secretion and is the evolving trait. Using an individual-based model of a spatially structured population, we show that permeability evolves through a collective mechanism. Environmental frequency is the primary determinant of evolutionary outcome. Under strong asymmetry, the dominant trait reaches a high plateau. The trait linked to the rare environment stays low. It rises smoothly as its environment becomes more frequent. Total permeability stays close to a fixed budget; environmental frequency mainly sets how it is split between the two traits. When the two environments are equally frequent, no single trait wins. Both traits coexist, and noise asymmetry between the two sensing channels biases the levels at which they coexist rather than selecting a winner. Coexistence is also the slowest outcome to reach. Higher noise speeds adaptation, but the evolved permeability is non-monotonic in noise, peaking at an intermediate value. Earlier work found that more noise favors collective sensing as long as cells are correct on average. We develop a two-trait adaptive-dynamics model that unifies these regimes. Away from symmetry, it reduces to a closed one-dimensional equation that captures the individual-based results. At symmetry, weak cross-repression gives a single coexistence attractor, consistent with replicate populations maintaining both traits.

This paper investigates AutoResearch, a protocol in which a coding language model edits a training program under a one-hour GPU budget and retains a change only if validation IoU improves. The protocol is applied to photovoltaic panel segmentation on a frozen real-image split, with DeepLabV3–ResNet-50 held fixed. Three campaigns of 24 experiments, using Gemma~4 12B, Qwen3-8B all improve their one-hour baselines, but retained modifications do not transfer across hardware. The Qwen3-8B configuration, trained on real images only, reaches a test IoU of 0.836 versus 0.833 for the reference GAN-augmented schedule. Research repository https://github.com/VU-AIML/automl4eo-autoresearch-segmentation.

Estimates of the quantum resources needed to run fault-tolerant algorithms are almost always reported as single numbers, even though they rest on uncertain hardware parameters and on cost models that disagree. We present an open, tool-agnostic framework that propagates evidence-based priors over fault-tolerant hardware parameters through five surface-code cost models, adds correlated-input sensitivity analysis, and evaluates the resulting intervals with a pre-registered three-layer protocol. Applied to RSA-2048, ECC-256, AES-256, and a Hubbard-model simulation on a superconducting surface-code architecture, it produces three coupled findings that together undermine the single-number convention. Propagating the error rates hardware has actually demonstrated, whose median across five large-array devices is about 4 x 10^-3 rather than the conventional 10^-3, widens the 90% physical-qubit interval to roughly forty times and lifts its median about 4.6 times above the conventional point estimate. Against the same inputs, five independently structured cost models, including two third-party estimators (the Azure Quantum Resource Estimator and Qualtran) that agree with each other to within about ten percent, disagree by a stable factor of two, a structural uncertainty that no single tool reveals. Most consequentially, both third-party estimators exceed their representable envelope for 80 to 100 percent of the evidence-based parameter space, and the AES-256 gate count overflows one tool's counter outright, so these workloads cannot be represented at measured error rates at all. The optimistic convention conceals every one of these effects. The uncertainty machinery we use is standard. The contribution is its evidence-based application, the pre-registered evaluation, and the finding that standard tools break down precisely where hardware operates.

Despite recent advances in humanoid locomotion, controllers optimized for command tracking and robustness tend to produce mechanical gaits, whereas controllers tied to human motion data often fail to generalize to commands outside the data distribution. This work introduces a learning framework that balances these competing objectives to synthesize real-time steerable, robust, and biomimetic locomotion policies from human data. Using an in-house curated locomotion dataset covering diverse speeds and directions, we first learn a natural locomotion prior policy through a teacher-student distillation process. Specifically, we train a full-body reference-conditioned policy with Reinforcement Learning (RL), then distill it into a lightweight prior policy conditioned solely on proprioception and a planar torso-velocity steering command. Next, we fine-tune the prior policy with multi-task RL to expand command coverage and robustness beyond the data distribution, pairing a goal-conditioned task that tracks arbitrary commands with a reference-guided task that tracks the human data as an explicit style regularizer. We validate our framework on three humanoid robots: the Boston Dynamics Atlas R1, Atlas D1, and Unitree G1. Experimental results demonstrate robust performance across real-world scenarios, including direct user-controlled locomotion in indoor and outdoor environments, and integration as the locomotion layer within hierarchical control stacks. Benchmarks against Tabula Rasa RL policies trained without human data and ablation studies confirm that our framework yields a lightweight, deployable policy that reconstructs coordinated whole-body behavior from a steering command, retaining the human gait characteristics while remaining robust and fully steerable.

We study the best arm identification problem in a stochastic environment with a novel form of adversarial perturbations, which we coin Shifting Means. While classically the mean rewards of the $K$ arms are stable in time, in Shifting Means only the gaps $\boldsymbol{\Delta}$ between mean rewards are stable, while their common shift may be determined adversarially in each round. The objective of the learner is to identify the best arm with high probability while minimizing sample complexity (the fixed confidence setting). Handling shifts requires new tools: we show that algorithms employing a Generalized Likelihood Ratio Test (GLRT) stopping rule, including the popular Track-and-Stop, fail under time-varying shifts. Instead, we propose Importance Weights for Shifting Means ($\mathsf{ISM}$). Assuming means bounded by $U$ and $\sigma^2$-sub-Gaussian rewards, we show $\mathsf{ISM}$ to be $\delta$-correct and to enjoy a sample complexity bound of order $K (\sigma^2 + U^2) \Delta_{\min}^{-2} \ln \frac{1}{\delta}$. We also present a matching (up to constant factors) worst-case lower bound and evaluate our results empirically.

Large-scale scientific simulations generate substantial data volumes, making lossy compression essential for reducing storage and data movement costs. However, users configure compressors through numerical error bounds (EBs) while often evaluating results using quality metrics and end-to-end performance. Because the relationship between an EB and these outcomes varies across datasets and compressors, identifying a suitable configuration typically requires exhaustive search, which can be time-consuming and computationally demanding. We present LOCAA, an Large language model-based scientific lossy compression auto-tuning agent that performs compression-in-the-loop search using tool-integrated execution, compressor-aware guidance, and persistent memory. LOCAA supports user-defined objectives and constraints without requiring a specialized search strategy. We evaluate LOCAA across three scientific applications, five compressors, and three use cases: fixed-ratio compression, compression tuning under multiple quality constraints, and compression tuning under quality and time constraints. For fixed-ratio search across twelve fields from two applications, LOCAA requires 1.98x fewer evaluation trials than binary search and 5.03x fewer than FRaZ on average. For compression ratio maximization under joint Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure constraints across six fields from the Community Earth System Model application, LOCAA reduces the average evaluation trials from 61.5 using binary search to 17, corresponding to a 72.4% reduction. Persistent memory further reduces the average number of trials by 27.9% across multiple timesteps of the same field. These results demonstrate the potential of tool-augmented LLM agents to provide flexible and efficient compressor tuning across diverse scientific data and user-defined objectives.

Anticipated applications of beyond sixth-generation (B6G) mobile broadband networks will require the co-design of communication and control subsystems within the network architecture. Existing co-design approaches are predominantly optimization-driven, integrating subsystems through joint optimization problems. While this approach is effective in relatively simple systems, such formulations present challenges in (i) modular subsystem representations, (ii) tracing the propagation of requirements across subsystems, and (iii) systematically analyzing design-space feasibility, particularly as the number and complexity of interacting subsystems increase. In this article, we present a compositional perspective on co-design based on the formal theory of co-design. We examine how the notion of composition introduced by this theory can address the challenges of the conventional optimization-driven approach. Building on this perspective, we propose a composition-driven methodology for communication-control co-design in B6G networks and illustrate it through a wireless-assisted robotic control case-study. We then discuss how the composition-driven and optimization-driven co-design approaches can complement each other and why this complementarity may be beneficial for B6G networks. Finally, we identify key research challenges and future directions toward the practical adoption of the proposed methodology.

We determine the sharp compactness ranges for the scalar-flat and minimal-boundary Yamabe problems on smooth compact manifolds of positive conformal type, excluding the conformal round hemisphere. For zero scalar curvature and positive constant boundary mean curvature, compactness holds through dimension $14$ for general boundary and dimension $21$ for umbilic boundary. For positive scalar curvature and zero boundary mean curvature, the corresponding upper dimensions are $14$ and $20$. Together with the noncompactness examples in Part I, these results identify the transition dimensions in both boundary classes. For positive scalar curvature, we also prove compactness through dimension eight for every fixed real boundary mean curvature, and obtain higher-dimensional ranges when this curvature is near zero or sufficiently large and positive. The proof combines scalar-correction estimates for the full conformal Fermi metric expansion with a geometric formula expressing the logarithmic coefficient of the corrected energy as a negative sum of squares.

We develop a regularized finite element method for the fractional conductivity equation, recovering the conductivity on an exterior observation region from noisy Dirichlet-to-Neumann measurements and using this reconstruction to determine the interior conductivity. Mesh-localized inputs and mass-lumped Tikhonov regularization discretize the exterior determination principle of Covi–Railo–Zimmermann (2026, Calc. Var. PDE). We prove exterior \(L^2\)- and \(L^\infty\)-convergence with error estimates, including the logarithmic correction at the critical Hölder exponent. The exterior reconstruction enables the Liouville reduction to the Calderón problem for the fractional Schrödinger equation. Separated measurements recover the interior potential, after which overlapping measurements determine the exterior potential tail. Together with the recovered exterior conductivity, the tail supplies the exterior Cauchy data for a Tikhonov-regularized finite element least-squares continuation. We prove \(H^s\)-convergence of the transformed conductivity and \(L^2\)-convergence of the interior conductivity, together with logarithmic state-bias and conductivity error estimates for full observation spaces. The admissible reconstructions remain uniformly positive and bounded. We present one- and two-dimensional numerical experiments illustrating the accuracy of the exterior and interior reconstructions and their sensitivity to measurement noise and discretization.

Sampling from a softmax distribution is a fundamental operation in machine learning, but its linear complexity in the number of items makes exact sampling impractical at scale. Two-level softmax (2LS) sampling is a popular alternative enabling sublinear-time sampling. Assuming items are partitioned into clusters, 2LS first samples a cluster and then an item within it. In this paper, we show that, despite its advantages, 2LS introduces systematic and undesirable sampling biases, which arise from misweighting clusters by ignoring both cluster size imbalance and intra-cluster similarity dispersion. We propose two sampling methods, Size-Corrected 2LS (S-2LS) and Size- and Dispersion-Corrected 2LS (SD-2LS), which correct these biases and provide provably better softmax approximations with negligible to non-existent computational overhead. In-depth experiments on five large-scale datasets validate the improved sampling properties of our methods. We recommend their consistent use in place of standard 2LS in future work.

Single-cell RNA-sequencing analyses predominantly use either Seurat (R) or Scanpy (Python), with the choice often driven by programming language preference. However, by default, these tools produce divergent variable features, neighbour graphs, clusters, and marker genes. Laboratories requiring Python, which supports most deep-learning, foundation-model, and agent tools, must re-implement Seurat analyses in a framework that does not replicate Seurat's results. Truecell was developed as a Python implementation of the Seurat interface, preserving function names, arguments, default settings, and the object model to facilitate seamless transfer of analyses. In eighteen paired end-to-end evaluations against R Seurat, deterministic outputs matched to floating-point precision, and fold-change order was identical across all nine differential expression tests. In a three-arm benchmark on three datasets, with fixed user parameters and 20 seeds per tool, Truecell more closely reproduced Seurat's clustering than a Seurat-configured Scanpy in all 12 combinations of dataset and resolution settings. Truecell's marker genes and enriched pathways were also closer to Seurat's than Scanpy's were, and pseudobulk DESeq2 reproduced Seurat's gene lists with a Jaccard index ranging from 0.95 to 1.00. This agreement reflects fidelity to Seurat rather than biological correctness.

Gaussian elimination with partial pivoting (GEPP) remains the most widely used solver for dense linear systems $A \mathbf x = \mathbf b$ for $A \in \mathbb C^{n\times n}$. We study the permutation $\pi = \pi(A)$ that arises in the GEPP factorization $PA = LU$, encoded by the permutation matrix factor $P = P_\pi$. When the input matrix is random, so is $\pi$. For random scalar butterfly matrices of size $2^n$ (a recursively defined family originally introduced to eliminate the need for pivoting altogether), we give the exact GEPP factorization and fully classify the induced permutation as an element of a $2$-Sylow subgroup of $S_{2^n}$ contained in the separable permutations. Moreover, the uniform-angle model induces the uniform distribution on this subgroup. For the GOE, GUE, and iid Bernoulli models, the induced permutation is never exactly uniform for $n \ge 2$. We give the precise rate of departure from uniformity at the leading pivot for the GOE and GUE, and give evidence that this non-uniformity vanishes asymptotically in the permuton sense. In contrast, for banded random matrices of sublinear bandwidth, including the tridiagonal $\beta$-Hermite ensembles, the induced permutation converges to the diagonal permuton. We further show that the resulting pivot probabilities are sensitive to implementation choices: standard LAPACK routines compare complex pivot candidates using the $\ell^1$ rather than $\ell^2$ norm, changing the GUE(2) pivot probability from $1/\sqrt3$ to $2/3$. Together these results establish a new connection between random matrix theory and permutation combinatorics through numerical linear algebra.

We prove that the mated-CRT map converges to Liouville quantum gravity under circle packing and the Riemann uniformization embedding. The proof is based on our recent work on circle packing and the Riemann uniformization embedding for random planar maps in ergodic-scale free environments, comparison of circle packing in different domains and several existing and new estimates for the mated-CRT map. As an intermediate step, we prove an extension of He and Schramm's result (1996) on convergence of circle packing maps to conformal maps to global uniform topology in several settings. The latter results are of independent interest and will be applied in our subsequent work on the convergence of spanning tree weighted planar maps to $\sqrt{2}$-LQG under circle packing and Riemann uniformization embedding.

A simulation of a real robot workspace must preserve task-relevant interactions, while policies developed in it must operate on observations available to the real robot. Yet scene reconstruction and policy development are often treated separately. We present Agentic Real-to-Sim-to-Real (Agentic RSR), a framework that links scene reconstruction, policy development, and real-robot execution through the same manipulation task. Given a workspace video, a task description, and a known robot model, an agent recovers metric scale, iteratively refines the scene using visual feedback, and checks task-relevant interactions in MuJoCo. A coding agent then develops an executable policy, progressing from privileged object poses to visual observations and randomized simulation. The policy can interleave multiple observations and actions within one invocation, while the agent uses execution feedback to continue, retry, or revise its approach. A shared task-level interface carries the policy and accumulated experience to the real robot, where fresh observations and safety checks guide execution. Using Claude Opus 5.5 through DeepSeek Harness (DSH), all 18 scenes across two robots pass the joint visual check; mean four-view Depth MAE against reference depth estimates is 0.0808 m, mean Lab $\Delta E_{76}$ is 8.01, and mean grayscale SSIM is 0.7338. In real-robot experiments, the aggregate task success rate reaches 80% of the simulation task success rate, indicating substantial retention of simulated performance on hardware. Code and reconstructed scene data will be made publicly available.

How can we predict which base checkpoint is worth an expensive round of agentic post-training? End-to-end pass@$K$ tests whether successful behavior already appears in a base model's distribution, but it is a poor fit for agentic coding: many base checkpoints cannot reliably produce the well-formed tool invocation required to complete a task end-to-end. Single-shot or short-horizon tasks avoid these tool-calling failures by collapsing a multi-step interaction into a fixed prompt and a single patch, but they sidestep the core capability we care about: maintaining coherent state over many tool-using steps as the repository evolves. To bridge this gap, we treat successful post-trained agent trajectories as a lookahead signal of base-model potential. Replaying each trajectory and rerunning tests after every code-changing step identifies the decisive step: the first step whose cumulative patch flips the repository from failing to passing, certifying that the recorded action solves the task given the prior context. Motivated by a coverage principle for agentic traces, we build three screens at this step that do not require a base checkpoint to drive the harness from a cold start: (i) Decisive-Action BPB (bits per byte) measures the probability mass on the certified action, (ii) Patch MCQ tests the checkpoint's choice between that action and alternatives rejected by the same verifier, and (iii) prefix-conditioned pass@$K$ evaluates support for functionally-correct generations and credits any continuation that the tests accept. Across ten pairs of public base and post-trained models, all three screens rank the cohort in close agreement with post-trained SWE-bench Verified pass@$1$. As our methods need only a benchmark's successful trajectories and its verifier, they can be applied to turn future agentic coding benchmarks into base-model evaluations.

We determine the hundredths digit of the real Grothendieck constant by proving $1.773 \leq K_G \leq 1.7799$. Furthermore, numerical heuristics suggest the estimate $K_G \approx 1.779$. We start by simplifying the Gaussian duality theory of $K_G$, based on Hermite projection games and Krivine rounding schemes. The bounds are obtained by a heuristic primal/dual search for these objects, followed by rigorous certification of their values. The search and certification are performed using AI tools, and in particular the rigorous certificates are very large (analytical reductions to thousands of numerical inequalities).

We introduce a mean-reverting stochastic differential equation with a three-component stochastic term and show that it generates a hierarchy of steady-state (stationary) distributions. At the top level, the hierarchy is described by a modified-Beta distribution, while one- and two-parameter reductions produce compact-support, power-law-tailed, and exponential-type limiting families within a single stochastic framework. We then construct two generalized extensions of this hierarchy. In the first, the power transformation is applied directly at the level of the stochastic differential equation; in the second, the same transformation is applied only after the stationary modified-Beta hierarchy has been obtained. While these two procedures agree on important lower branches and limiting cases they generally differ at the top level. The generalized hierarchy is therefore not unique: nonlinear transformation and stationary-state reduction do not commute. For both routes, we derive the probability density and cumulative distribution functions, express their parameters in terms of the underlying stochastic dynamics, clarify the relations among their limiting cases, and compare the resulting families with the traditional Generalized Beta framework.

We introduce the local approximation propert (LAP) and prove that it characterizes Oka manifolds. We prove that LAP yields convex approximation and, in an $n$-dimensional target, propagates across sets of zero $(2n-1)$-dimensional Hausdorff measure. Consequently, strong dominability characterizes Oka manifolds, convex approximation in the target dimension suffices, the Oka property is local in the Euclidean topology, and it descends under surjective holomorphic maps. Local families of entire curves give geometric applications: smooth projective rationally connected manifolds are Oka, and deleting an algebraic subset of codimension at least two from any such manifold preserves the Oka property. Structure theorems further show that compact Kähler manifolds with nonnegative holomorphic sectional curvature or nef tangent bundle are Oka. Finally, the complement of a smooth degree-$d$ hypersurface in $\mathbb{P}^n$ is Oka exactly when $d\leq n+1$.

We study approximately uniform sampling of satisfying assignments from random $k$-SAT formulas. For every sufficiently large $k$ and density $0 < \alpha \le 2^k/k^{16}$, we prove that, with high probability over the formula, there is a sampler whose output distribution is within total variation distance $\varepsilon$ of the uniform distribution on satisfying assignments and whose expected running time is at most $(nk(\alpha+1)/\varepsilon)^C$, for a universal constant $C$. Our algorithm improves the counting and sampling algorithms obtained by Chen, Lonkar, Wang, Yang, and Yin (STOC 2025) at the density $2^k/\operatorname{poly}(k)$ with running time $(n/\varepsilon)^{\operatorname{poly}(k,\alpha)}$. Our result achieves this density region for sampling with a polynomial degree independent of both the width and the density. Our algorithm separates a high-degree core from the remaining variables, and combines a recursive sampler for the residual formulas with approximate block heat-bath updates on the core. We adapt the recursive insertion-chain framework of Jain, Mizgerd, and Pham (2026) from $2$-trees to ordinary connected violation sets. Expansion and random literal signs yield uniform moment bounds for the resulting correlated lists across all residual formulas, allowing the signed-flow analysis to give a universal polynomial running-time degree. A polymer expansion and an exploration bound establish a polynomial spectral gap for the core dynamics.

Cell viability assessment is a core requirement in cell culture systems, with critical applications in biopharmaceutical manufacturing and drug development. Conventionally, it is measured by adding membrane-impermeable dyes to a sample (a process called staining), which allows compromised cell membranes to be distinguished from intact ones. However, staining has several limitations: (a) chemical agents can perturb normal cellular processes of the cells being measured, (b) it is often ambiguous to assign viability to individual cells whose membrane integrity is only partially compromised, (c) photobleaching can undermine measurement accuracy over time when using fluorescent stains, and (d) staining cannot be performed in situ or in real time. Here, we show that (1) stained cells captured under brightfield imaging contain sufficient information to distinguish live and dead cells, and (2) cells captured under unstained brightfield imaging exhibit similar image features to their stained counterparts, enabling models trained on stained cells to generalize to unstained ones. We then report the development and validation of ViabiLens, an AI-assisted software tool for label-free cell viability analysis. ViabiLens combines a cell detection model for localizing individual cells with a convolutional neural network (CNN) classifier for live/dead prediction, paired with an interactive UMAP-based viewer for visualizing and exploring individual cells across the sample. Evaluated on Chinese Hamster Ovary (CHO) cells spanning a wide range of viability conditions, ViabiLens achieves a mean absolute error of 2.33% on unstained samples against fluorescence-based reference measurements. The demo of ViabiLens software is available at https://amirrezavazifeh.github.io/ViabiLens-Project-Page/.

Throwing objects that generate aerodynamic lift can greatly extend robot throwing beyond ballistic flight. A returning boomerang is a challenging example because its flight depends strongly on the release velocity, attitude, and spin, while robotic manipulators cannot readily reproduce the rapid motions used in human throwing. We present a model-based framework for robotic boomerang throwing centered on the release state. We identify the boomerang flight dynamics in stages to predict how flight changes across design variations. To systematically design the robot throwing motion, we screen candidate parameters according to how strongly and consistently they control release spin under uncertain contact conditions. These models are then used to design the throwing motion and boomerang for a 6-DoF manipulator with limited joint speeds. To our knowledge, this is the first robotic manipulator to generate a returning boomerang flight. In the demonstrated returning trial, the boomerang is released at 51 rad/s (8.1 rev/s), reaches 2.03 m from the robot base, and returns to touch down 0.31 m from the base. The successful release differs significantly from the measured human throws, showing that a robot need not imitate human throwing motion to achieve a returning flight. The project page is available at https://robot-boomerang.github.io

The apparent absence of a stabilizer-specific phase-space description for qubit systems is not fundamental, but arises from fixing a state-independent discrete Wigner map. Allowing the phase-space representation to adapt to the state through a simple optimization procedure, we prove that every qubit stabilizer state admits an exact delta-function discrete Wigner representation for any fixed phase-space partition. This optimization can be implemented directly at the level of measurement statistics by selecting maximal probabilities across mutually unbiased bases forming the partition. This construction naturally leads to a non-stabilizer witness defined by the optimized value of the Wigner function at the origin. Stabilizer states saturate the universal lower bound of this witness for pure states, whereas a value strictly larger than the bound certifies non-stabilizerness. Although the witness is not a finite-size resource monotone, it becomes sharply concentrated and effectively invariant under random Clifford transformations in the large-qubit limit, suggesting an asymptotically linear growth law for broad families of non-stabilizer states. Our results restore a meaningful geometric phase-space characterization of qubit stabilizer structure and provide an operational diagnostic of non-stabilizerness.

Quadruped robots can traverse low obstacles, but many 2D planning pipelines still model obstacles as binary occupied regions and rely on sampling-based search that can be inefficient under a limited budget. We propose a perception-assisted height-adaptive planning framework based on CMP-IRRT*, a Channel Mamba PointNet-guided Informed RRT* planner. Given a calibrated top-view RGB observation, the perception module estimates obstacle regions and converts depth predictions into a ground-relative height map. The planner then performs height-conditioned collision checking, treating high obstacles as blocked while allowing low obstacles to be traversed, and uses the CMP guide to bias sampling toward promising regions while retaining standard free-space and informed sampling fallbacks. Experiments on 2D planning benchmarks show that CMP-IRRT* reduces explored nodes and iterations compared with classical and neural-guided baselines, and a controlled ablation supports the contribution of the Mamba-based guide. In constructed traversability-aware scenarios, the proposed planner reduces path length by up to 16.3% when low obstacles are traversable, and a Unitree Go2 demonstration further shows executable bypassing and traversal behaviors. Our code is publicly available at https://github.com/MingfanZhao/height-adaptive-planner.

We study Bernoulli percolation and its universality classes on hierarchical lattices generated by edge iterated graph systems (EIGS). By examining eight critical exponents, we prove that no finite family of substitution-multiplicative dimensions completely determines universality, providing a rigorous proof of the failure of dimension-based universality discussed by Hauser and Saxena [Phys. Rev. B 34 (1986), 8193-8195]. Although the six exponentials theorem provides number-theoretic criteria for scale commensurability, we further disprove the conjecture that critical-exponent universality requires commensurate discrete renormalisation scales.

Deployments of research agents are moving to populations of thousands that share one pool of compute, while most current systems organize one project at a time or leave the population unorganized. We argue that such a population will acquire an organization whether or not its designers provide one, so designers should provide it explicitly, and that the multi-agent systems community holds the tools to do so. We propose a society of agents, a population of persistent agents under explicit institutions, and develop it for science as a society of researchers built on six principles. Principal investigators compete for compute through requests for proposals, independent review, and grants; a human governor, the mayor, allocates resources and assigns no tasks. In a running society of ten thousand researchers, asked only to improve the pretraining of language models, one lab reported a way to reach the same quality with about 30% less compute, a result the labs that tested it do not yet agree on. We close with six open problems for the agents community.

We study the two-dimensional anisotropic three-state Potts ferromagnet on the square lattice using Wolff single-cluster Monte Carlo simulations and finite-size scaling. For coupling ratios $\lambda=J_y/J_x=0.5$, $0.75$, and $1$, finite-size scaling of the correlation ratio yields critical behavior consistent with the two-dimensional three-state Potts universality class. The scaling of the leading Fisher zeros gives a correlation-length exponent consistent with $\nu=5/6$, while their cumulative density is consistent with the expected specific-heat exponent $\alpha=1/3$. We further characterize the anisotropy at criticality using directional correlation ratios $R_x$ and $R_y$ together with directional FK wrapping probabilities. For $\lambda=0.5$ on a physically square lattice, $R_x$ and $R_y$ approach distinct critical values while yielding a common correlation-length exponent. From the wrapping probabilities, we independently determine an effective aspect ratio $\rho_e^\square=0.6413(5)$, in close agreement with the theoretical value $\rho_e^{\square,\mathrm{th}}\simeq0.64150030$ obtained from the isoradial representation. Using the theoretical value to set the physical aspect ratio restores directional equivalence, $R_x\simeq R_y$, and brings the overall correlation ratio toward the isotropic-square reference. The results show that spatial anisotropy changes the effective critical geometry without altering the bulk three-state Potts universality class.

Covert communication conceals wireless transmission activity, but conventional multi-antenna designs rely mainly on spatial beamforming and can be constrained by limited spatial degrees of freedom. This paper investigates polarization-reconfigurable antenna (PRA)-aided multiple-input multiple-output (MIMO) covert communication, where Alice and Bob perform transmit and receive polarforming, respectively, and Willie uses a vertically polarized antenna for radiometric detection. We jointly optimize the transmit covariance matrix and the transmit and receive phase shift vectors to maximize Bob's achievable rate under the covertness and transmit power constraints. Under Gaussian signaling, perfect polarized channel state information, and known noise power at Willie, we derive his optimal radiometric threshold and exact minimum detection error probability (DEP) for a finite observation length, and convert the DEP requirement into a deterministic constraint on his received signal power. We further prove that, for a fixed transmission design, positive signal leakage becomes detectable as the observation length tends to infinity. To solve the design problem for a finite observation length, we develop an alternating optimization (AO) algorithm with a generalized water-filling covariance update and closed-form phase updates. Numerical results validate the exact DEP analysis and the rapid convergence of the proposed algorithm. Compared with the sufficient divergence-based condition, the exact covertness constraint permits a $0.99$–$1.12$~dB higher received signal-to-noise ratio (SNR) at Willie, while joint transmit and receive polarforming provides a rate gain of up to $53.8\%$ over the considered benchmark schemes.