Papers

Dephasing can drive a quantum Boltzmann sampler into an ordered phase while its programmed probability distribution remains disordered. We trace this transition to an enhanced conditional response: coherence loss changes how each spin responds to its neighbors, and interactions amplify the change. For all-to-all coupling, we establish the stationary transition at finite dephasing. Near criticality, the magnetization distribution depends on the ratio of dephasing strength to the square root of system size, retaining a finite imprint of coherence even as the local coherent correction vanishes. In the strong-dephasing limit on a square lattice, the dynamics generates effective multispin interactions and probability currents, with Ising-like critical statistics. Adjusting the local dissipative update restores the target probability process on arbitrary graphs.

We study global energy minimization for matrix-valued heteroclinic connections whose vacuum sets are continuous conjugacy orbits rather than isolated points. For two distinguished parameter regimes of a one-dimensional $\mathrm{SU}(5)\times\mathbb Z_2$ matrix field model, we first identify the full zero set of the quartic potential as the disjoint union of two compact homogeneous vacuum orbits. We then construct auxiliary potentials controlled by the Frobenius distance to these orbits. Pointwise comparison with the original potential, combined with a calibration inequality and the one-dimensional coarea formula, gives a sharp lower bound for every finite-energy connection joining the two vacuum components; no diagonality, commutativity, or symmetry-reduced ansatz is imposed on the competitors. Two explicit non-Abelian kinks attain the bound and are therefore global minimizers in the full orbit-to-orbit heteroclinic classes. Their exact wall tensions are $4\sqrt2\,\mu^3/(3\lambda)$ and $9\sqrt2\,\mu^3/(10h)$, respectively. Equivalently, the corresponding line-segment paths realize the degenerate weighted distance between the vacuum manifolds. We also resolve every fixed-endpoint sector: for arbitrary prescribed representatives on the two vacuum orbits, the energy infimum is the same wall tension, and it is attained if and only if the prescribed representatives form a closest pair of the two orbits. Nonclosest endpoint sectors therefore exhibit non-attainment through increasingly slow tangential motion along the vacuum manifolds. The proof separates a model-independent distance–coarea criterion from the model-specific orbit geometry and polynomial positivity estimates, providing a reusable mechanism for matrix-valued multiwell potentials with symmetry-generated vacua.

Data attribution methods using gradient similarity are widely used to analyze and select training data for large language models, but what gradient similarity actually measures is debated. Some interpret it as identifying task-relevant skills, while other work reports that surface form is the main factor. We resolve this debate for supervised fine-tuning examples by varying task and answer format independently. Specifically, we render benchmarks in different answer formats, such that datasets can share a task without a format or a format without a task. We find that gradient alignment follows the answer format, as benchmark pairs sharing an answer format align strongly (disattenuated cosine near 0.4), while same benchmarks rendered with different answer format classes show no alignment (near 0.0). We demonstrate that this ordering holds from the earliest pretraining checkpoints through post-training, and across model scales and families. We then analyze the released selections of LESS, a gradient-based data selection method for instruction tuning, and find that each target's selections over-represent the target's own answer format. Hence, we demonstrate that gradient-based attribution methods track format similarity more than task semantics, meaning that such methods, as well as the semantic interpretation of the gradient, should be tested on data where answer format and task vary independently for greater robustness and reliability.

Mechanical intelligence, loosely defined as the reduction in control burden afforded by a robot's physical form, has become a prominent concept in robotics, with instantiations in bioinspired robotics, soft robotics, robotic swarms, and many other areas. However, rigorous theoretical understanding and quantitative measures of mechanical intelligence have lagged behind the engineering systems that the community has developed. In this work, using modern legged robots as a benchmark and exemplar, we propose several information-theoretic metrics for quantifying mechanical intelligence. By viewing body dynamics as both a computational process and a communication channel, we show that several prior insights in legged-robot engineering can be described using information theory, and we quantify how bits are processed by mechanical modes and across robot coordinates. Specifically, we examine the trade-off between explicitly incorporating compliance through series-elastic actuation and using so-called proprioceptive, low-gear-ratio transmissions, and we explore how these mechanisms interact with control policies during locomotion. We develop these results on systems of increasing complexity: a simplified linear model of a robot-leg transmission, a nonlinear single-leg simulation, and simulated quadruped robots controlled by a learned policy while navigating challenging terrain. These results lay the groundwork for broader study of robot mechanisms and their role in embodied computation.

To keep coding agents from going off the rails, production systems now review each proposed action with a blocking monitor that can reject it before it runs (Auto Mode in Claude Code, Guardian in OpenAI's Codex). Prior evaluations of such monitors largely measure robustness to accidental harm or prompt injections from untrusted sources looking to hijack the agent. Less understood is how they hold up when the agent they monitor is persistently misaligned. To understand this risk, we task an adversarial agent with evading production blocking monitors and causing catastrophic harm, e.g. by exfiltrating its own weights. We find that when instructed with high-level attack strategies, adversarial agents can succeed through several distinct mechanisms, such as agent-generated prompt injection against the monitor, multi-agent attacks, and malicious compaction. In particular we find that in 79% of trials, the agent can use an injection attack against Auto Mode and Guardian to run arbitrary bash commands. We also find that it is possible to greatly improve Auto Mode through design changes like enhancements to tool coverage, changes in transcript formatting, and the addition of an agentic monitor stage. Even with these improvements, preventing multi-context attacks at an acceptable cost remains an open problem. By detailing our red-teaming methodology and highlighting new attack vectors, we aim to help defenders evaluate their mitigations against the possibility of persistent malign coding agents. Code is available at https://github.com/safety-research/red-teaming-auto-mode.

Small-business owners need expert guidance on their own terms, across schedules, languages, and channels, but low premiums make exceptional, continuous human service uneconomic for much of the market. Combining public evidence, Kinro operational data, and an illustrative five-year service model, we show why traditional brokerage economics leave 35 million U.S. small businesses underserved. An AI-native brokerage can change those economics by performing and coordinating routine work continuously, while licensed professionals govern consequential exceptions and the brokerage remains accountable.

In mental health care, reasoning over patient journeys is a key task for clinicians. Yet these journeys, encompassing a longitudinal progression of biological, psychological, and social events, are often spread across disparate unstructured text narratives, making temporal recovery challenging. We present CliniCIRCA, a multi-stage LLM framework for Calendar-anchored, Imprecision-aware Reconstruction of Clinical Annals. To our knowledge, CliniCIRCA is the first to temporally classify clinical events across unstructured discharge summaries without event-level timestamps. From 14,882 MIMIC-III mental health admissions, we first construct a benchmark of 52 discharge summaries on which CliniCIRCA produces 15,891 temporally tagged events. After correcting 629 errors based on a clinician-in-the-loop evaluation, we produce verified gold-standard labels. Finally, the corrected timelines drive a temporally grounded summarization stage that compresses each source 1.52 times into a date-grouped chronological record. We then scale the framework to generate 1,000 silver-standard timelines and evaluate them as training data. Compared with zero- and few-shot prompting, instruction tuning generally improves five open-weight models on event extraction, temporal tagging, and summarization across silver and clinician-verified evaluations.

Permutation invariant polynomials (PIPs), together with related polynomial-based invariant descriptors such as fundamental invariants (FIs), are widely used in constructing high-fidelity global potential energy surfaces (PESs) of molecules that contain identical atoms. Although the monomial symmetrization approach (MSA) enables fast evaluation of PIPs through recursive factorization, it leads to deeply nested computational graphs that may require large memory and are inefficient in modern automatic differentiation frameworks. In this work, we introduce JaxPIP, a JAX-based implementation that reformulates PIP/FI evaluation into tensorized linear algebra operations. By replacing recursive factorization with dense matrix operations combined with log-exp transformation and segmented summation, the evaluation becomes regular and GPU-friendly. This allows efficient execution with just-in-time compilation and enables large-scale batch evaluation of energies and forces (as well as higher-order derivatives). The resulting architecture supports ensemble simulations such as quasi-classical trajectory (QCT), path-integral molecular dynamics (PIMD), and diffusion Monte Carlo (DMC) in a fully vectorized manner. As demonstrated in examples, JaxPIP provides a practical route for efficient simulations of molecular systems with scalable GPU execution.

LLVM is the cornerstone of modern compilers, but its subtle intermediate representation (IR) semantics make transformations error-prone and necessitate formal verification. Alive2, a state-of-the-art translation validator based on satisfiability modulo theories, has achieved substantial success in automating the validation of LLVM transformations. However, it still faces scalability limitations, does not support symbolic bitwidths, and offers only bounded guarantees for loops. In contrast, interactive theorem provers such as Lean can address these cases but require substantial proof engineering. In this paper, we present Trivet, a framework combining large language models (LLMs) and Lean for automated translation validation of LLVM transformations. Trivet generates structured proof scaffolds based on source and target functions, automatically discharges obligations amenable to deterministic reasoning, and delegates transformationspecific obligations to LLMs. It produces refinement proofs or counterexample-based refutations, with every successful verdict checked by the Lean kernel. On 148 LLVM transformations, Trivet verifies or refutes 147, leaving one invalid case unresolved. Successful cases include 60 loop-free transformations with symbolic bitwidths, 27 cases from a restricted class of loop-containing transformations, and 10 complex valid fixed-bitwidth cases on which Alive2 times out. Compared with an unscaffolded baseline, scaffolding enables 26 additional proofs. On cases solved by both configurations, it reduces mean proof time by 75.9% and mean monetary cost by 88%.

Assembly, wear, and component replacement perturb the sensor extrinsics and joint zeros encoded by a humanoid CAD model. Existing procedures calibrate one sensor pair or require external fiducials. Using only robot-native motion and onboard sensing, we present OmniCalib, a target-free workflow that calibrates the full upper limbs—all 14 arm joint zeros and the extrinsics of both wrist and chest cameras—as well as lower limbs and the multi-camera head rig. Each module matches a robot-native task to a parameter block, checks observability, and writes only supported corrections to the CAD model. Our depth ICP method recovers all 14 arm joint zeros and calibrates all RGB-D camera extrinsics without any calibration target. Relative to CAD, the estimated extrinsic corrections are 10.56 mm and 1.74 degrees for the left wrist, 6.33 mm and 1.25 degrees for the right wrist, and 9.81 mm and 0.929 degrees for the chest RGB-D camera. ICP point-to-plane residual is 2.09 mm. On the same injected offsets, ICP and ArUco recover all 14 joint zeros below the 0.1-degree encoder-resolution reference. On an AGIBOT A3 Ultra humanoid, four static double-support stances recover all 12 lower-limb joint-zero offsets injected with an RMS error of 0.063 degrees. The head module combines multi-camera visual odometry with legged odometry and dynamic compensation through the live ROS transform tree. Using only planar walking, it attains a mean SO(3) error of 1.061 degrees across three sequences. The best sequence reaches 0.775 degrees, competitive with iKalibr at 0.902 degrees from rich 6-DOF excitation. Rig-relative angles repeat within 0.140 degrees. Injection recovery and held-out tests validate each observable block.

People present different aspects of themselves across relationships. Computational work has captured such variation in communication style. But this variation also extends to which principles people foreground or background in a particular relationship–i.e., in the values they express and how they balance them. We conceptualize these relationship-specific expressions of values as demonstrated values. To make demonstrated values visible, we introduce Value Faces, a system that analyzes a person's existing chat histories from their everyday messaging platforms using Schwartz's ten basic human values and produces separate value profiles for their different relationships. In a mixed-methods study(N=18), we find that the resulting value profiles distinguished participants' relational contexts with twice the odds of guessing, while system-inferred differences across relationships aligned with participants' perceptions of those differences. Participants used these profiles to articulate previously implicit differences in how they presented themselves, connect them to roles and changes over time, and reconsider their self-assessments.

In Part~I of this tutorial, we showed that introducing angular dispersion (AD) into a collimated optical pulse allows for tuning the wave packet group velocity in free space. In principle, the group velocity can take on arbitrary values, whether superluminal, subluminal, or even negative. However, any significant deviation of the group velocity from $c$ (the speed of light in vacuum) necessitates propagation at large angles with respect to the optical axis in the non-paraxial regime. In Part~II of this tutorial, we describe the recent discovery of a new form of AD we refer to as `non-differentiable AD', which circumvents the limits imposed by conventional (differentiable) AD. Non-differentiable AD does not refer to an AD profile that is discontinuous, contains a kink, or features a singularity. Rather, a non-differentiable AD profile is continuous, smooth, and is differentiable everywhere except for one wavelength at which the derivative is not defined. We show that salutary features follow from this non-differentiability with respect to tuning the group velocity of a pulsed beam in free space; namely, significant deviations in the group velocity away from $c$ are achievable in the paraxial regime while remaining free of group-velocity dispersion and all higher-order dispersive effects. This tutorial presents an outline of these recent results for tuning the group velocity of a wave packet via non-differentiable AD, connecting them with the corresponding results associated with conventional AD – as outlined in Part~I. Moreover, we show that non-differentiable AD undergirds the unique characteristics of propagation-invariant space-time wave packets, thus unifying a large swathe of results in a single conceptual framework.

Vision-language-action (VLA) models let robots follow language instructions, but their language backbones of several billion parameters are the main obstacle to running them on robot hardware. Structured pruning reduces that backbone, and removing 63% of it from OpenVLA-OFT drops LIBERO-Long success from 93.2% to 0.8%. A recent approach restores such a model with supervised fine-tuning followed by reinforcement learning, which needs online rollouts and hundreds of GPU-hours. We recover most of the lost success entirely offline. Width pruning narrows the blocks but keeps the residual stream at its original size, so teacher and student hidden states have the same shape and are matched directly, without a projector. Training against a cache built in one teacher pass lifts the 63%-reduced student to within 3.5 points of the teacher in about 8 GPU-hours. A sweep over nine ratios locates where the recovery objective starts to matter. Up to 45% reduction the two do not differ significantly on OpenVLA-OFT. Hidden-state distillation then adds +2.1 to +4.5 points there between 63% and 87%, and +9.4 to +22.1 points on CogACT from 63% onward. At 81% on CogACT, a tripled recovery budget narrows the distilled student's gap to the teacher to 3.9 points on average, while supervised recovery stays more than 20 points below. At matched compression, width pruning yields higher success and depth pruning lower latency. On a 6-DoF manipulator, the distilled student at 72% reduction reaches 77.5% success against 59.5% for supervised recovery, runs 2.23x faster on-board than the teacher, and uses 62% less memory.

Various theoretical mass models have consistently achieved impressive accuracy in reproducing experimental masses. However, their predictions in unmeasured neutron-rich regions exhibit noticeable model dependence. In this study, we systematically investigate the differences in model predictions by comparing the liquid-drop mass terms of two representative models. Using two widely used models, Weizsacker-Skyrme-type (WS4) and Duflo-Zuker-type (DZ10), as representative examples, we find that the differences in an isotope chain gradually become more remarkable with increasing neutron number, not only for total binding energies but also for individual mass terms. The most noticeable difference appears in the volume-symmetry energy. By leveraging the term-by-term differences between the liquid-drop energy components of WS4 and DZ10, we introduce a machine learning gating network that adaptively combines the two models to improve predictive accuracy. This conditional hybrid model achieves a lower root-mean-square deviation (rmsd) than either model alone, reducing the overall rmsd from 0.284 MeV (WS4) and 0.560 MeV (DZ10) to 0.232 MeV. In the future, this term-by-term comparison strategy can be extended to models based on density-functional theories.

Teleoperation, a human-in-the-loop control scheme, allows a human operator to remotely command and guide a mobile robot to navigate in off-road environments, yet fluent and user-friendly tele-navigation requires an alignment of traversability evaluation between human and robot. In the teleoperation system, the human operator typically utilizes off-site incomplete and delayed feedback via a human-machine interface to make a judgment of traversability, while the robot makes such an evaluation based on in situ onboard sensory information, which could cause divergent traversability estimation and thus generate mismatched decisions and actions. Existing approaches for traversability modeling, estimation, and prediction are mainly derived from the view of robots, i.e., robot-centric, and are practically suitable for fully autonomous mobile robots, but neglect the influence of human operators. To address this problem, this paper extends the concept of traversability from robot-centric to human-centric by accounting for the operator's cognitive states, such as attention, workload, and risk tolerance or awareness, termed tele-traversability. We first revisit the definitions and roles of traversability in robotics and then extend them to teleoperation settings. Finally, we highlight future trends and open challenges of tele-traversability toward human-centric teleoperation systems.

A plane-wave optical pulse travels in free space at a group velocity $c$ (the speed of light in vacuum) measured along its propagation axis. It is sometimes thought that spatially structuring the field in free space reduces the group velocity below $c$ because – intuitively – the oblique wave vectors undergirding the wave packet increase the average group delay. Here we show that spatiotemporally structuring a pulsed optical beam (or wave packet) can yield – in principle – arbitrary group velocities in free space in contradistinction to this commonly held intuition. We devote our attention here to pulses endowed with angular dispersion (AD) where the propagation angle is wavelength dependent. This class of wave packets is particularly pertinent because their group velocity is constant over the transverse field profile and along the propagation axis, thereby yielding an unambiguous group delay. However, significant deviation of the AD-induced group velocity in free space from~$c$ inevitably requires a large numerical aperture that lies deep in the non-paraxial regime, and such wave packets experience AD-induced group-velocity dispersion. The formulation presented here captures a broad range of results, connecting them in a single framework. In Part~II of this tutorial, we describe recently identified `non-differentiable AD' (associated with propagation-invariant space-time wave packets) that helps circumvent the limits associated with conventional (differentiable) AD as outlined here.

This paper studies the cluster-assignment layer of a cluster-first-route-second decomposition for the capacitated pickup-and-delivery problem with time windows (CPDPTW), instead of a direct route-ordering quadratic unconstrained binary optimization (QUBO). Sample-based subspace diagonalization (SQD) degenerates to best-of-shots for any diagonal optimization Hamiltonian, so a useful transfer to routing requires non-diagonal relaxation. Quantum random access optimization (QRAO) provides this non-diagonality by encoding binary variables through non-commuting quantum random access code (QRAC) observables. CPDPTW-derived conflict graphs expose a routing-specific obstruction because dense objectives and penalty-encoded constraints destroy QRAO compression. We keep the Hamiltonian sparse by encoding only the sparsified objective and enforcing one-hot, capacity, and cluster time-budget feasibility by repair after rounding. We make no quantum-advantage claim. Under strong repair the classical pass alone reaches near-optimal cost at the tested sizes. The result is a regime map linking sparsification, achieved compression, linear-combination-of-unitaries (LCU) 1-norm, heavy-hex two-qubit depth, sampling drift, and final routing quality on Qiskit Aer, calibrated FakeTorino, and IBM Heron ibm_quebec. Across a 108-row ideal-calibrated-hardware evaluation grid spanning four to twelve pickup-delivery request pairs, the hardware slice has mean gap 0.0016 and mean device-vs-ideal total variation distance (TVD) 0.279; a decoder ablation at sizes six through twelve isolates the non-diagonal signal.

We study T-odd effects through two-photon exchange in semi-inclusive deeply inelastic scattering in the kinematic region where the produced hadron has a low transverse momentum. The absorptive part of lepton-quark scattering amplitude is calculated. Transverse momentum dependent factorization is performed with the absorptive part. Although the absorptive part is divergent, the physical results, i.e., the obtained differential cross-section, is finite. Including the T-odd effects, the differential cross section receives new contributions which have different angular dependence than that obtained with one-photon exchange. Certain asymmetries can be introduced to detect the T-odd effects. Our results here are not only relevant to detecting new effect beyond the one-photon approximation in the process but also relevant to searching for new physics at lepton-proton colliders.

Growth curve models are widely used in psychological research, and variable selection can help identify baseline characteristics associated with longitudinal heterogeneity. However, conventional inference after data-driven variable selection can be invalid because the same outcome data are used for both selection and inference. We develop a data-fission framework for post-selection inference in growth-curve models that separates the information used for selection and inference while retaining all participants in both stages through the addition and subtraction of Gaussian noise. The framework accommodates flexible variable-selection procedures and targets covariance-weighted linear projection parameters in the selected working model. It provides exact inference when the covariance structure is known, and we establish asymptotic validity under suitable regularity conditions when the covariance structure is estimated. Simulations show that the proposed method provides valid inference and improves efficiency over subject-level data splitting, whereas naïve post-selection inference can be biased. An application to the Longitudinal Study of American Youth illustrates the proposed framework.

The microscopic origin of the low-field $1/9$ magnetization plateau in spin-$1/2$ kagome antiferromagnets remains unresolved. Here, we show that chemical pressure reshapes the hierarchy of fractional magnetization plateaus in the titanium-based kagome family $\mathrm{Cs_8AB_3Ti_{12}F_{48}}$ ($A=\mathrm{Rb},\mathrm{Li}$; $B=\mathrm{K},\mathrm{Na}$). High-field magnetization measurements up to 60 T reveal a robust $1/9$ plateau-like phase in the expanded $\mathrm{Cs_8RbK_3Ti_{12}F_{48}}$ and $\mathrm{Cs_8LiK_3Ti_{12}F_{48}}$ compounds, despite the absence of the conventionally more robust $1/3$ plateau. In contrast, compressed $\mathrm{Cs_8LiNa_3Ti_{12}F_{48}}$ exhibits neither the $1/9$ plateau-like phase nor a quantum-disordered ground state. Specific-heat measurements and first-principles calculations show that lattice expansion preserves a frustrated, fully connected kagome exchange network and gapless quantum-disordered ground states, whereas compression reorganizes the exchange network into weakly coupled quasi-one-dimensional subsystems and induces successive magnetic transitions. These results demonstrate that the $1/9$ and $1/3$ plateaus need not share a common microscopic origin and suggest that the $1/9$ plateau may represent a more universal feature of frustrated spin-$1/2$ kagome magnetism.

Kilojoule-class short-pulse (< 10 ps) lasers are excellent tools for generating relativistic ion beams, but achieving high laser-to-ion conversion efficiency remains an open challenge. Recent experiments show a significant increase in conversion efficiency when leveraging targets with an average plasma density approaching the relativistic-critical limit. We present an analytical model that explains this increase by extending the theory of target-normal sheath acceleration (TNSA) to include laser penetration of relativistic-critical density targets, enabling energy transfer to the ion front by heating the expanding electron sheath. This physical process increases the sheath field strength and significantly improves ion cutoff energy and laser-to-ion conversion efficiency relative to classical TNSA. The model predicts a maximum ion conversion efficiency of 37% by optimizing laser transmission and target areal density. Key scalings of the model agree with particle-in-cell (PIC) simulations and published experimental data. A series of 2D and 3D simulations of hydrocarbon plasmas confirm the robustness of the acceleration process, demonstrating a path for maximizing ion yields using relativistic-critical targets.

Traditional dialogue systems for social robots require both dialogue strategies and user attribute recognition, each demanding specialized expertise. However, data collection is costly in real-world deployments, and the resulting datasets often include many failure cases. In this study, we aim to automate the acquisition of dialogue strategies by leveraging both successful and failed interactions using a vision-language model (VLM) and a large language model (LLM). We propose an architecture in which user attributes, recognized by the VLM, along with dialogue history, are fed into the LLM to generate dialogue strategies tailored to specific user attributes. We extracted dialogue strategies from an interaction dataset collected through a field experiment and evaluated their effectiveness. The results demonstrate that explicitly representing failure strategies complements success strategies and improves performance. Our findings highlight a practical pipeline for constructing and maintaining an interpretable strategy repository from in-the-wild deployment logs by recycling abundant failure interactions as reusable constraints, ultimately reducing the development cost of social robots.

Disease severity classification for genetic conditions is subjective and labor-intensive, creating bottlenecks in genomic screening, where commercial panels vary widely in size and overlap. We developed an autonomous AI agent integrating Reasoning and Acting (ReAct) with Retrieval-Augmented Generation (RAG) to classify 10,211 Human Phenotype Ontology terms. It uses American College of Medical Genetics (ACMG)-endorsed severity guidelines and American College of Obstetricians and Gynecologists (ACOG) quality-of-life criteria to retrieve PubMed literature, generate interpretable reasoning chains, and independently verify claims. At the phenotype level, using expert-curated cohorts, the agent achieved 93.55% accuracy (MCC 0.9237) with 82.6% to 91.4% of claims supported by direct evidence or valid inferences. Gene-level severity was aggregated across 8,738 pairs, identifying 3,283 autosomal recessive pairs with severe or profound presentations. External validation showed 95.2% concordance with Mackenzie's Mission gene list. This system enables standardized panel design by providing reliable, automated classification supported by direct evidence.

We study infinitesimally homogeneous affine manifolds with prescribed structure groups. First, for the real symplectic group $\operatorname{Sp}(2n,\mathbb R)$, we prove that the corresponding infinitesimally homogeneous structures are precisely flat torsion-free symplectic affine structures. Second, for \(\operatorname{U}(n)\times\{1\}\), whose \(G\)-structures are equivalent to almost contact metric data, we classify the torsion-free characteristic tensors and obtain the general torsional case by invariant deformation. The admissible torsion and inner-torsion parameters are governed by a single algebraic relation, and the horizontal distribution is contact precisely when a certain combination of these parameters does not vanish. We also describe the compatible connections and relate the torsion-free branches to trans-Sasakian geometry.

An interior penalty nonconforming finite element method is developed for a strain gradient elasticity (SGE) model in arbitrary dimensions, using an $H^1$-nonconforming displacement element built from vector-valued quadratic polynomials enriched by divergence-free face bubbles. Rigorous analysis establishes optimal and robust error estimates with respect to both the Lamé coefficient $\lambda$ and the size parameter $\iota$. The underlying divergence-commuting structure further leads to nonconforming finite element Stokes complexes in two and three dimensions. Numerical experiments support the predicted convergence behavior and parameter robustness, while a circular-hole benchmark under uniaxial tension illustrates the applicability of the method to a multiply connected domain.

This study investigates the multi-thermal structure of solar jets by combining extreme ultra-violet (EUV) and Ha observations, addressing whether cool and hot components originate from the same jet, their morphological similarities and differences, and the role of mini-filaments. We analyze 70 jet events simultaneously observed by Atmospheric Imaging Assembly (AIA) and Chinese Ha Solar Explorer (CHASE) from 2023 May 25 to 2026 January 15. The events are classified into four types based on whether or not there are significant differences between the two wavebands in terms of length and width; nonlinear force-free field extrapolations are applied to examine magnetic fields. We find that the cool and hot components correspond to different temperature parts of a unified jet, showing spatiotemporal coincidence and kinematic synchronization. Morphologically, 30% show no significant difference in length/width, 37% differ in one dimension, and 33% differ in both. About 80% involve mini-filament eruptions; jets with filaments more often exhibit morphological differences (filament non-expansion, hot shell thickness, insufficient kinetic energy, or material rarefaction). In contrast, jets without filaments tend to show consistent morphologies; when discrepancies occur, they are mainly linked to small magnetic field curvature, which reduces magnetic tension and leads to less acceleration of cool material. These results highlight the complex interaction between thermal, dynamic, and magnetic factors in shaping jet morphology.

Aligning and maintaining complex optical beam paths is a central challenge across experimental science, because it is a high-dimensional task with strong cross-coupling between controls, often in systems with limited physical access. We present an automated hardware-software framework that resolves this alignment challenge using low-cost, retro-fittable motorized mounts driven by projective-geometry models and a photodiode-fed optimizer. A compact forward model describes the beam path to paraxial order with only the physical mirror angles left free, so it can be rapidly ($\sim$ms) numerically inverted to return the required mirror angles for a desired beam trajectory. A photodiode-fed optimizer then fine-tunes this geometric starting point, and converged mirror settings are tabulated for retrieval in milliseconds and actuation in seconds. We experimentally demonstrate the performance of this approach on a retro-reflected lattice atom-transport system, yielding improvements in both speed and precision over manual alignment. This framework reduces the manual effort required to align complex beam paths, enables programmable optical control in experiments with limited physical access, and enhances the scalability of complex optical architectures.

Wasserstein barycenters provide a notion of weighted mean for probability measures on a metric space. We prove that the barycenter curvature-dimension condition ${\rm BCD}(K,N)$ is equivalent to ${\rm RCD}(K,N)$ for $K\in \mathbb R$ and $1<N<\infty$. This gives a new characterization of Riemannian curvature-dimension spaces by entropy inequalities at barycenters of finite families of measures. As a byproduct, we introduce an almost ${\rm BCD}$ condition that allows an additive error in the entropy inequality. It is stable under measured Gromov-Hausdorff convergence and implies essential non-branching when the error is sufficiently small. The resulting class contains non-Riemannian Finsler spaces. Within the ${\rm BCD}$ framework, this answers an open problem posed by Ambrosio in his 2018 ICM survey. We further bound the failure of the parallelogram identity for cotangent norms in terms of the entropy error.

We construct braided Hopf algebroids in a braided monoidal category over a field $k$ and study its properties using graphical representation. Then we study Ehresmann-Schauenburg Hopf algebroids assocaited to braided Hopf Galois extensions. We introduce braided Lie-Rinehart algebras which generalize the definition in \cite{ALP24, ALP23, ALP25} and study its universal enveloping algebra under symmetric condition. In particular, we introduce Lie-Rinehart algebras (braided Lie-algebroids) associated with braided Hopf algebroids in the category of the module of a triangular Hopf algebra. We then focus on the case for braided Ehresmann-Schauenburg Hopf algebroids and study their right invariant vector fields, which turn out to be isomorphic to the $H$-equivariant vector fields on the quantum principal bundle (Hopf Galois extension) as Lie-Rinehart algebras. Finally, we introduce braided jet Hopf algebroids associate to braided Hopf algebroids in the case that the source and target subalgebra belong to the braided center. Moreover, we show there is a dual pairing between the $k$-order universal enveloping algebra of the braided right invariant vector fields and the $k$-th jet space of a braided Hopf algebroid and further more a skew pairing between the universal enveloping algebra of its braided right invariant vector fields and its jet Hopf algebroid under a finiteness condition.

In this work we present an experimental demonstration of one-dimensional Fourier-domain imaging using a fully-digital wirelessly coordinated coherent distributed antenna array (CDA) receiver. The nodes consist of two software-defined radios (SDRs) operating with independent system clocks performing wireless time, frequency, and phase coordination without a shared reference such as the global navigation satellite system (GNSS). Two spatially separated noise sources transmit independent noise waveforms with a bandwidth of 25 MHz and a carrier frequency of 915 MHz. Two sources were positioned at angles of $-6.28{\deg}$ and $12.95{\deg}$ off broadside and imaging was performed. The two sources are clearly resolved to within $3{\deg}$ of their expected locations in both the individual and combined source measurements and demonstrating the Fourier-domain image reconstruction principle using a fully-digitally coordinated distributed antenna array.