Papers

Teaching robotics relies on screen-based simulation, showing robot motion in an abstract coordinate frame rather than at real scale in the learner's own space, while access to physical hardware is limited by cost, safety, and scheduling constraints. We present MR-Robotics LAB, a mixed-reality (MR) platform that replays MATLAB-generated robot trajectories at real scale within the learner's physical environment. A browser-based service validates a MATLAB workspace file (.mat), normalizes units, and publishes a versioned JSON trajectory; a Unity application on a Meta Quest 3 then reproduces the authored joint configurations under position control and replays them at the declared frame rate within a physics-enabled scene that supports collision detection and end-effector grasping. A formative single-group evaluation with engineering students found that participants reported low setup effort (M = 4.67 on a 5-point scale) and perceived support for workspace understanding from multi-viewpoint inspection (M = 4.56), and 83% of participants affirmed their willingness to use the platform in an introductory robotics course. The evaluation instrument records only perceived outcomes, without counterbalancing or a learning measure, so no comparative advantage over desktop simulation is claimed. The contribution is a reusable simulation-to-MR trajectory pathway and design guidance for hardware-free robot visualization in engineering education.

We give two small generating sets for the subgroup of the mapping class group of a non-orientable closed surface which is generated by Dehn twists and acts trivially on the $\mathbb{Z}_2$ coefficient first homology group of the surface.

Extensive occlusions in real-world scenarios pose challenges to gait recognition due to missing and noisy information, as well as body misalignment in position and scale. We argue that rich dynamic contextual information within a gait sequence inherently possesses occlusion-solving traits: 1) Adjacent frames with gait continuity allow holistic body regions to infer occluded body regions; 2) Gait cycles allow information integration between holistic actions and occluded actions. Therefore, we introduce an action detection perspective where a gait sequence is regarded as a composition of actions. To detect accurate actions under complex occlusion scenarios, we propose an Action Detection Based Mixture of Experts (GaitMoE), consisting of Mixture of Temporal Experts (MTE) and Mixture of Action Experts (MAE). MTE adaptively constructs action anchors by temporal experts and MAE adaptively constructs action proposals from action anchors by action experts. Especially, action detection as a proxy task with gait recognition is an end-to-end joint training only with ID labels. In addition, due to the lack of a unified occluded benchmark, we construct a pioneering Occluded Gait database (OccGait), containing rich occlusion scenarios and annotations of occlusion types. Extensive experiments on OccGait, OccCASIA-B,Gait3D and GREW demonstrate the superior performance of GaitMoE.OccGait is available at https://github.com/BNU-IVC/OccGait.

More than 300 million people worldwide are affected by one of over 7,000 known rare diseases, yet diagnosis remains difficult because patients initially present with incomplete and heterogeneous phenotypes. We present HPOQuest, a training-free framework for sequential phenotype acquisition in rare-disease diagnosis. Starting from a small set of observed patient phenotypes, HPOQuest maintains a probabilistic disease ranking and iteratively selects informative follow-up questions to support clinicians during patient assessment. Confirmed phenotypes update the disease ranking, while all responses update the candidate question set. Across four benchmark cohorts, HPOQuest substantially improves diagnosis from sparse initial phenotypes, with gains of up to 30% points at Recall@1 and 45% points at Recall@5. These results demonstrate that sequential phenotype acquisition can substantially improve rare-disease diagnosis from limited initial clinical evidence.

Modeling physical dynamics, including how objects move, interact, and change state, is central to video world models for embodied AI. We present StrucPhysVideo, a family of video world models that bridges physics-focused data curation with language- and action-conditioned prediction of scene evolution. Our data pipeline combines motion-aware video segmentation, quality and content filtering, and physical relevance verification with structured annotations of objects, materials, and temporally localized interactions. By disentangling camera motion from object behavior and explicitly describing contact, deformation, and state transitions, the pipeline provides supervision grounded in observable physical events. Building on these data, we introduce StrucPhysVideo-TI2V, a sparse Mixture-of-Experts (MoE) text-image-to-video model trained with a curriculum that progressively emphasizes physical dynamics while retaining general-domain video data. StrucPhysVideo-TI2V achieves state-of-the-art performance on Physics-IQ Verified, scoring 45.5% and outperforming Cosmos3-Super-Image2Video by 2.8 percentage points. Caption ablations across backbones further demonstrate the effectiveness of physics-focused supervision. We further extend StrucPhysVideo-TI2V to StrucPhysVideo-IA2V, an interactive image-action-to-video world model that predicts visual outcomes from robot end-effector commands. Action conditioning, causal autoregressive generation, and few-step distillation enable incremental robot rollouts with only four denoising steps. Together, StrucPhysVideo advances physical dynamics modeling from image- and language-conditioned video prediction toward action-driven interaction.

There is a natural connection between the SOS rank problem for bi-quadratic forms and the Zarankiewicz extremal problem for C4-free bipartite graphs. The classical Zarankiewicz number z(m,n) controls the bipartite skeleton associated with monomial squares. Allowing two cells to form a single bilinear square leads to augmented Zarankiewicz configurations and the second-order Zarankiewicz number z2(m,n). Unlike zRL and zSL, defined through recursive sufficient conditions, z2 maximizes over all irreducible displayed SOS decompositions without imposing (RW 3+). Hence, to prove z2(m,n)<=R, one must prove that every simple limited configuration with more displayed squares is reducible; failure of a sufficient condition cannot serve as a counterargument. We prove z2(4,4)=10, z2(7,4)=19, z2(8,4)=21, z2(5,5)=17, and obtain z2=zSL=zRL in all these cases. The extremal irreducible 6x4 configurations with 16 displayed squares form a single isomorphism class under row and column relabeling, whereas the extremal irreducible 7x4 configurations with 19 displayed squares form exactly three isomorphism classes. The four-column results form a structural chain: classify lower-order extremal configurations first, then use hereditary irreducibility under deletion of complete squares to constrain the next order. Finite exhaustive steps use candidate pruning, a necessary compatibility graph, clique enumeration, and orbit reduction, with a verifiable reducibility or irreducibility proof for each remaining orbit. For 5x5, there are two ordinary extremal skeletons; finite exclusion leaves only two highly symmetric 18-square candidates. They define the same ten-square polynomial, which admits an explicit nine-square representation, yielding the upper bound for z2(5,5).

Core-ionization induced charge migration in molecular systems has been widely studied, but the influence of relativistic effects on such dynamics remains relatively unexplored from a relativistic theory perspective. This issue is particularly important because core orbitals exhibit strong scalar-relativistic and spin-orbit imprints, and these effects are further enhanced in heavy-element systems, where relativistic signatures also alter the valence orbitals. To address this, we formulate four-component Dirac-Coulomb and two-component atomic mean-field exact two-component Hamiltonian approaches for studying charge migration within real-time time-dependent density functional theory. The time-dependent induced electric dipole moment is used as a marker of the characteristic charge-migration time scales. We apply the method to nitrosobenzene (N $1s$ electron removal), iodoacetylene (I $2p$ electron removal) and interhalogen series (I $2p$, Cl $2p$ electron removal). For iodoacetylene, the charge migration timescale is relatively insensitive to the choice of Hamiltonian but they show weak relativistic phase and amplitude modifications. However, it would be misleading to conclude that relativistic effects are generally unimportant. In interhalogen systems, we observe significant deviations between relativistic and non-relativistic dynamics. These results demonstrate that relativistic signatures in core-ionization-induced charge migration are not determined by heavy-atom core ionization alone, but by the relativistic sensitivity of the valence orbital manifold that drives core-hole screening and charge redistribution. Moreover, consistently across all systems, we observe a delay in the emergence of the relativistic imprints.

We investigate the complete set of twist-3 gluon generalized parton distributions (GPDs) of the nucleon at nonzero skewness within a spectator model, in which the nucleon is treated as a two-body system consisting of an active spin-1 gluon and a spin-1/2 spectator particle. The spectator mass is allowed to vary continuously and is described by a spectral function, while the nucleon-gluon-spectator coupling is modeled by an effective vertex containing two form factors. We calculate the twist-3 gluon GPDs over a broad kinematic range and investigate the corresponding impact-parameter-dependent parton distributions, defined as two-dimensional Fourier transforms of the GPDs at zero skewness. In the forward limit, we further obtain the corresponding twist-3 parton distribution functions (PDFs). Our results provide model predictions for twist-3 gluon GPDs and PDFs that can be useful for future phenomenological studies and for investigating observables at current and future collider facilities.

We prove that $L^2(\Omega)$ admits no Riesz basis of exponentials when $\Omega$ is a ball in $\R^n$, $n\geq2$, or a nondegenerate triangle in $\R^2$. The ball result extends to every nonempty bounded convex open set with $C^2$ boundary in $\R^n$, $n\geq2$. Starting from a hypothetical Riesz basis, we use Beurling weak limits of translates of its frequency set to construct a stationary system. On the associated Hilbert space, we define spectral cutoff projections and a comparison family of orthogonal projections obtained from the synthesis operator. The distance between corresponding projections is uniformly bounded by a constant strictly smaller than one. The comparison family is continuous in operator norm, whereas the boundary geometry of $\Omega$ produces two strong limits of the cutoff projections with strictly nested ranges. Both limiting projections would then be at distance less than one from the same comparison projection, which is impossible.

The article proposes the possibility of determining the magnitude of a future earthquake with high accuracy, based on the frequency data of VLF/LF electromagnetic emissions, as a diagnostic precursor that existed before an earthquake. Such magnitude will contribute to significantly improving the research of various fundamental issues in seismology in the future.

Benford's law specifies a marginal distribution for significant digits, whereas the usual first-digit Pearson $p$-value is calibrated under an independent multinomial sampling model. We separate these statements with four constructions that share the same one-time or pooled Benford target but have different joint structures. Under a wrapped-Gaussian circular Markov construction, the nominal 5% Pearson test rejects 21.6% of samples at a fixed persistence level even though every one-time marginal is exactly Benford; a sequence-level second-order moment-matching calibration reduces the rejection rate to 4.8%. The same strategy performs well in the randomized-rotation and random-composition designs. The effect persists across changes in sample size and sequence length, and a grid approximation to a continuous log-significand Cramér-von Mises discrepancy shows the same design dependence. In the wrapped-Gaussian design examined here, corrected procedures retain rejection probabilities that rise with the size of a smooth marginal departure. Finally, we distinguish calibration from an information boundary: significand-only methods cannot detect changes that leave the complete significand process unchanged, but they readily detect perturbations that alter it. Benford conformity is a marginal statement; a Benford $p$-value is valid only relative to a specified statistic, sampling law, and calibration procedure; an integrity claim requires substantive competing models.

Accurate characterization of stimulated Raman scattering (SRS) remains a critical challenge in inertial confinement fusion (ICF), as SRS not only scatters laser energy but also generates suprathermal electrons that preheat the fuel and degrade implosion performance. Conventional backscatter diagnostics provide direct measurements of SRS but cannot collect the entire scattered-light signal, limiting the accurate characterization of SRS strength. Using a non-local thermodynamic equilibrium collisional-radiative model with a double-Maxwellian electron distribution, we systematically investigate how suprathermal electrons modify the titanium K-shell x-ray emission spectra. The spectra exhibit high sensitivity to the suprathermal-electron fraction at relatively low bulk electron temperatures, making them particularly suitable for diagnosing suprathermal electrons during the early stage of ICF, when even a small suprathermal-electron population can compromise fuel compression. The calculated spectra reproduce experimental measurements from the Nova Laser Facility with good agreement, and the inferred suprathermal-electron fractions show improved consistency with independently measured SRS losses compared with the original spectral analysis by Glenzer~\href{https://doi.org/10.1103/PhysRevLett.81.365} {\text{[S. H. Glenzer et al., Phys. Rev. Lett. 81, 365(1998)]}}. These results demonstrate that K-shell spectroscopy, combined with accurate NLTE collisional-radiative modeling, provides a reliable probe of SRS strength in laser-produced plasmas. Hence, this approach may be extended to spatially resolved diagnosis of SRS strength, offering a promising complement to conventional backscatter diagnostics.

At the fluid surface, an asymmetric wave field generated by an oscillating body produces thrust in what is known as wave-driven propulsion (WDP). Although this thrust is directed forward, the vertical oscillations inevitably produce waves radiating outwards in all directions. The effect of these side waves is not accounted for in simplified models focused on the fore–aft wave field. In this work, we take a two-dimensional shallow water approach, deriving thrust and power expressions that account for surface waves emitted in any direction. Supported by an analytically driven approach, we pose a numerical optimisation problem to maximise thrust, imposing appropriate Sommerfeld boundary conditions across subcritical and supercritical velocity regimes. The two-dimensional set-up allows us to understand how the side waves emitted by the body contribute to thrust and efficiency. Furthermore, we explore how maximal thrust depends on the shape of the body beginning with a square followed by ellipses of varying aspect ratios. Using these learnings, we include the shape of the body as a control variable to demonstrate how an optimised shape can lead to further thrust and efficiency gains.

We prove the half-plane one-arm exponent for critical Bernoulli bond percolation on the square lattice. Ikhlef and Ponsaing obtained an exact formula for the probability that the unique infinite percolation hull running along an odd-width strip passes through a prescribed boundary edge. Their interpolation, however, treats a rational function as a polynomial. We clear the full denominator, prove a coordinatewise Laurent-degree bound directly at $q^3=1$, and establish the exact strip formula from the deletion relations. At the homogeneous point, the qKZ expression is the Bernoulli probability of this boundary-passage event. A finite local modification, the RSW theorem, and one-arm quasi-multiplicativity then give, uniformly for $1\le r<R$, ${\bf P}_{1/2}(A_1^+(r,R))\asymp (r/R)^{1/3}$.

Aims. We explore the dynamics of the Northern and Southern Taurid meteoroid streams to identify major mechanisms structuring the evolution of the streams. Methods. We use chaos maps and numerical simulations to explore the dynamics of the streams. We also perform some semi-analytical analysis to confirm the mechanisms we identified in the maps. Results. We show how Northern Taurids are structured by the von Zeipel-Lidov-Kozai mechanism and how it interacts with several mean-motion resonances with Jupiter. This mechanism is visible as an increase in inclination for most particles, which is less prominent for those trapped in mean-motion resonances. It is especially strong for larger initial semi-major axis within the stream. We specifically study the 7:2 mean-motion resonance with Jupiter to confirm it leads to observable swarms. Furthermore, we explore the influence of non-gravitational forces, showing that they blur the influence of mean-motion resonances but not the von Zeipel-Lidov-Kozai mechanism. We also show that the dynamics of the Southern Taurids are very similar to the Northern Taurids.

Latent neural operators improve the efficiency of operator learning for partial differential equations (PDEs) by performing the main computation on compact latent representations. However, directly compressing the input representation to obtain such compact representations may discard solution-relevant spatial information, especially for PDE solutions with multiscale structures. To address this problem, we propose HiLNO, a hierarchical latent neural operator that constructs a fine-to-coarse-to-fine latent space and further introduces multi-scale supervision (MSS) and anisotropic Gaussian attention. The hierarchy mitigates potential information loss during compression, while MSS aligns intermediate predictions with downsampled target fields, encouraging solution-relevant structures to be captured across multiple spatial scales. Anisotropic Gaussian attention enables feature transfer across the hierarchy, making HiLNO applicable to general geometries. Experiments on representative PDE benchmarks and a large-scale automotive aerodynamics task show that HiLNO achieves competitive predictive accuracy, while reducing the parameter count by an average of 84.4% and FLOPs by an average of 69.2% compared with LinearNO. Additional experiments demonstrate effective generalization to unseen spatial resolutions. Code is available at https://github.com/JcLimath/HiLNO.

We investigate the existence conditions for coupled extremal Kähler metrics on minimal ruled surfaces over a genus 2 Riemann surface. Using the Calabi ansatz to reduce the coupled extremal equations to ordinary differential equations, we prove that a pair of coupled extremal metrics exists for normalized Kähler classes $\Omega_a$ and $\Omega_b$ if and only if their parameters $(a, b)$ belong to an explicitly defined open region $\mathcal{S}_{\mathrm{ext}}$ in the positive real quadrant. Furthermore, we show that this existence region inherently contains the diagonal segment corresponding to classical extremal Kähler metrics.

Multi-turn agent trajectories often contain redundant rounds (failed tool calls, parallel sub-queries, verification-only steps) that inflate both training and inference cost. We propose viewing each trajectory as a round-level dependency DAG that exposes which rounds are globally load-bearing for the final answer, and fine-tune agents on trajectories refined through this DAG. Given an LLM-annotated DAG, these edits are deterministic and interpretable, with optional rephrasing. Models trained on these refined trajectories consistently outperform those trained on the original trajectories at lower inference cost. Specifically, across four multi-modal QA benchmarks, our refinements improve downstream accuracy by up to $1.7$\,pp over vanilla SFT (and $5.7$\,pp over an LLM-deletion baseline) while reducing per-sample inference messages by up to approximately $40\%$ and inference tokens by up to approximately $48\%$, translating to substantial savings in compute and serving cost. Code is available.

Stochastic subspace methods have gained popularity as gradient descent based techniques for large scale optimisation problems, especially in distributed settings. In this paper, we introduce the technique of "persistence of memory" to greatly extend and improve the random subspace methods. To this end, we leverage a vector that is only weakly correlated with the gradient in order to provide a guiding structure to the generative process of the random subspace along which the descent is going to take place. This guidance vector may be fixed for a large number of iterations, only to be refreshed at wide intervals (on whose size we can provide guarantees in terms of problem parameters). In important machine learning settings, such as optimisation problems embodying sparsity or a minibatch structure, we show that the guidance vector can be obtained in an effective and computationally inexpensive manner by leveraging the structured properties of the problem. En route, we establish to our knowledge the first theoretical analysis of classical SSD methods for sparse functions. In a local neighbourhood of the optimum, we demonstrate an alignment phenomenon of our gradient estimates with a low-lying eigenvector of the Hessian, allowing a once-for-all computation of the guidance vector which renders the method computationally favourable even in scenarios with unstructured objectives.

Computed tomography (CT) has been widely used in medical examinations and non-destructive testing. Micro-CT (microfocus X-ray CT system) is an advanced version that can observe the internal structures of small objects. However, secondary radiation can prevent micro-CT from imaging the full structure of the object. Given the same amount of secondary scans as primary scans, simple subtraction solves the problem at the price of doubled acquisition time. To reduce the acquisition time, one aims to limit the secondary scans to as few imaging angles as possible and interpolate to recover the missing data. Different interpolation methods have been explored for limited-angle tomography, such as polynomial or spline interpolation, compressive sensing, deep learning, etc. In contrast to many of these scenarios, the secondary imaging setup considered in this paper often exhibits simple sinusoidal structures that are not exploited directly by any of the aforementioned approaches. This paper aims to fill this gap with a continuous mathematical model describing the secondary sinogram only with information from the projection space. Building on this model, we propose an interpolation method that effectively interpolates secondary scans from limited observations.

Let $m$ be a non-negative integer and $f(x)$ a positive, non-decreasing function satisfying certain conditions. We give an explicit lower bound for the number of integers $n\leq x$ such that $\#([n, n+f(n)] \cap \mathbb{P})=m$ for sufficiently large $x$, where $\mathbb{P}$ denotes the set of prime numbers. This work extends the results of Mastrostefano and of Freiberg, and also makes the lower bound of Masrtrostefano explicit. In addition, we show that if the interval length is sufficiently large, then there exist infinitely many bounded intervals of the same length that contain exactly a prescribed number of primes.

What is a gait? Appearance-based gait networks consider a gait as the human shape and motion information from images. Model-based gait networks treat a gait as the human inherent structure from points. However, the considerations remain vague for humans to comprehend truly. In this work, we introduce a novel paradigm Vocabulary-Guided Gait Recognition, dubbed Gait-World, which attempts to explore gait concepts through human vocabularies with Vision-Language Models (VLMs). Although VLMs have achieved the remarkable progress in various vision tasks, the cognitive capability regarding gait modalities remains limited. The success element in Gait-World is the proper vocabulary prompt where this paradigm carefully selects gait cycle actions as Vocabulary Base, bridging the gait and vocabulary feature spaces and further promoting human understanding for the gait. How to extract gait features? Although previous gait networks have made significant progress, learning solely from gait modalities on limited gait databases makes it difficult to learn universal gait features for practicality. Therefore, we propose the first Gait-World model, dubbed {\alpha}-Gait, which guides the gait network learning with vocabulary knowledge from VLMs. However, due to the heterogeneity of the modalities, directly integrating vocabulary and gait features is highly challenging as they reside in different embedding spaces. To address the issues, {\alpha}-Gait designs Vocabulary Relation Mapper and Gait Fine grained Detector to map and establish vocabulary relations in the gait space for detecting corresponding gait features. Extensive experiments on CASIA-B, CCPG, SUSTech1K, Gait3D and GREW reveal the potential value and research directions of vocabulary information from VLMs in the gait field.

The survey discusses the problem of measuring correlations in composite quantum and statistical systems. After briefly recalling the standard methods of describing correlations, the emphasis is on the method of correlation indices. The latter method for quantifying the strength of correlations in composite physical systems is sufficiently general allowing for measuring in a unique way the correlation strength in both quantum and statistical systems, for static as well as for dynamic processes. The correlation indices, can be defined for correlation operators, reduced density matrices, and other operators containing information on correlations in the studied composite systems. The correlation indices measure all types of correlations, quantum correlations, such as entanglement, as well as classical correlations. They are applicable for characterizing static as well as dynamical processes. Examples are given of correlation indices for several quantum states and for spin and pseudospin systems. The quantification of correlations in a nonequilibrium system is exemplified by calculating the correlation index for a trapped Bose-Einstein condensate subject to the action of an alternating field.

Agentic browsers can execute security-sensitive actions under a user's authenticated session, making indirect prompt injection and deceptive confirmation interfaces a direct threat to action integrity. Existing human-in-the-loop (HITL) safeguards are insufficient when the approval prompt itself can be influenced by untrusted page content or model-generated text. We present the Verifiable Action Card (VAC), an architectural defence that reconstructs approval information from the ground-truth pending browser action and trusted intent provenance, renders it out-of-band in the trusted browser chrome, and binds approval to the exact action re-verified at dispatch. VAC combines provenance fencing, a ground-truth action descriptor, default-deny confirmation, provenance-aware risk gating, and execution binding. We implement VAC in a complete agentic browser and evaluate it on a 24-scenario benchmark covering confused-deputy attacks, Lies-in-the-Loop dialog forging, indirect prompt injection, adaptive action substitution, provenance evasion, and legitimate tasks. Across the evaluated LLMs, attack success without VAC ranges from $68\%$ to $100\%$, whereas VAC reduces attack success to $0\%$ on every model, with $78\%$ legitimate-task completion and a $0\%$ false-block rate. These results show that grounding approval in the action that will actually execute provides architectural protection against security failures that prompt-level defences and conventional HITL confirmation cannot reliably prevent.

We study higher-order differential equations corresponding to integrals of the Dotsenko–Fateev type and associated with four-point correlation functions with degenerate fields $\Phi_{n,1}$. We determine the general structure and coefficients of the equations in terms of the integral parameters $ \{ A,B,C,g \} $. In particular, special cases of these equations in CFT are used for verification. In addition, the relationship between higher-order differential equations and hypergeometric operators is established.

Indirect quantum control aims to manipulate a target system through interventions on an auxiliary controller with which it interacts. We formulate finite-step indirect-control protocols using the language of higher-order quantum operations, representing admissible controller manipulations as deterministic superinstruments. This representation separates the uncontrolled but fixed dynamics from the controllable operations and allows the optimal control problem to be written as a semidefinite program for a chosen figure of merit. The resulting optimum gives an operational benchmark by providing the best performance achievable by a finite sequence of control operations, including protocols with classical or quantum feed-forward. More restricted and experimentally motivated control classes, such as independent unitary controls or memoryless quantum channels, can then be compared against this benchmark. We illustrate the framework with a two-step qubit-purification task, in which an initially mixed target qubit is steered toward a pure state through a fixed interaction with a controller qubit. The example shows regimes where simple unitary strategies saturate the higher-order benchmark, as well as regimes where they are provably suboptimal. This approach provides a systematic way to study the value of control resources in indirect quantum-control schemes.

The Andromeda galaxy (M31) exhibits a systematically low star formation efficiency (SFE) compared to other star-forming galaxies. Star formation is thought to be regulated by the mass of gravitationally bound gas. To investigate whether the low SFE in M31 originates from a scarcity of such bound gas, we analyze the dynamical state of its giant molecular cloud (GMC) population by estimating their virial parameters ($\alpha_{\rm vir}$). Using a JCMT-SCUBA2 850 micron dust-continuum GMC catalog as the parent sample, we combine it with IRAM 30 m CO(1-0) data to define a working sample of 173 GMCs and derive their kinematic properties. Most analyzed GMCs exhibit high $\alpha_{\rm vir}$, indicating that they are predominantly gravitationally unbound at the approximately 86 pc resolution of our observations. While no statistically significant global correlation is found between SFE and $\alpha_{\rm vir}$ for the full cloud sample, the upper quantiles of the SFE distribution show progressively stronger negative trends with increasing $\alpha_{\rm vir}$. This upper-tail trend may arise from the combined effects of the virial parameter limiting the upper range of SFE values accessible to the GMC population and feedback-driven disruption reducing the number of high-SFE, high-$\alpha_{\rm vir}$ CO-bright clouds in the observed sample. The substantial scatter in the SFE-$\alpha_{\rm vir}$ plane likely reflects the diverse evolutionary stages of GMCs, the temporal mismatch between gas and star formation tracers, and the limitations of a cloud-averaged virial parameter as a tracer of internal dynamical structure, making a simple one-to-one correspondence between $\alpha_{\rm vir}$ and instantaneous SFE difficult to recover for individual GMCs.

Weekly influenza surveillance counts guide vaccine distribution and public-health alerts, yet they are hard to forecast. Each region offers only a few seasons, waves shift in timing and height every year, and information that helps while a wave grows misleads after its peak, whereas last season's shape stays informative for a year. Existing epidemic graph models and general forecasters read a short fixed window and treat all past information alike, so they neither exploit earlier seasons nor discard stale associations when the epidemic phase changes. To address these limitations, we propose TERN, a forecaster built around a delta-rule fast-weight memory that decays channel-wise and erases along a learned address under gates driven by local epidemic-phase features, combined with an explicit seasonal reference and online adaptation. On three Cola-GNN influenza benchmarks, TERN outperformed epidemic graph models and general forecasters, matched or exceeded seasonal references, and a controlled comparison confirmed the contribution of the memory itself.

Recovering 3D human body motion from video is important for applications such as rehabilitation assessment and sports performance evaluation. For prosthesis users, this requires capturing both natural body joints and the geometry of the prosthetic device, a challenge that existing methods are not designed to address. Model-based estimators rely on body models trained on non-amputee individuals and cannot represent prosthesis geometry, while model-free methods lack body kinematic priors and are unreliable under occlusion. This challenge is particularly prominent for users of running-specific prostheses (RSPs), where the RSP has a complex curved geometry and moves dynamically during exercise. To fill this gap, we collect RSP3D, the first 3D dataset of RSP users, covering essential daily-life and exercise actions from participants with varied amputation conditions, using a multi-camera marker-based motion capture setup. We formally define the task of prosthesis-aware 3D pose estimation, evaluate representative methods in a zero-shot setting, and confirm their individual limitations. We further propose a hybrid baseline combining model-based body joint estimation with model-free RSP shape recovery, establishing a starting point for future research.

In this paper, we study the following linearly coupled Kirchhoff-Choquard system in $\mathbb{R}^3$: \begin{align*}\left\{\begin{array}{l} &-\left(a_1+b_1\int_{\mathbb{R}^3}|\nabla u|^2\,dx\right)\Delta u+V_1(x)u=\mu(I_{\alpha}*|u|^p)|u|^{p-2}u+\lambda v,\quad x \in \mathbb{R}^3,\cr &-\left(a_2+b_2\int_{\mathbb{R}^3}|\nabla v|^2\,dx\right)\Delta v+V_2(x)v=\nu(I_{\alpha}*|v|^q)|v|^{q-2}v+\lambda u,\quad x \in \mathbb{R}^3,\cr &u, v \in H^1(\mathbb{R}^3), \end{array}\right. \end{align*} where $a_1, a_2, b_1, b_2, \lambda, \mu,$ and $\nu$ are positive constants. When the potentials are constant functions, the author previously proved the existence of positive ground state solutions in the following cases: the noncritical case $\frac{3+\alpha}{3}<p\le q<3+\alpha$, the upper half critical case $\frac{3+\alpha}{3}<p<q=3+\alpha$, and the lower half critical case $\frac{3+\alpha}{3}=p<q<3+\alpha$, by using the Nehari-Pohozaev manifold method (NoDEA Nonlinear Differential Equations Appl.33(2026)). In the present paper, we extend these results to the case of nonconstant potentials. Under suitable assumptions on $V_1(x)$, $V_2(x)$, and $\lambda$, we prove the existence of nontrivial ground state solutions. In the noncritical and upper half critical cases, the main tools are Jeanjean's monotonicity trick and a global compactness lemma. For these cases, we establish a refined version of the splitting lemma by relaxing the standard growth assumption at the origin from $o(|t|)$ to the optimal $o(|t|^{\alpha/3})$, thereby significantly broadening the applicable class of nonlinearities. In contrast, for the lower half critical case $p=\frac{3+\alpha}{3}$, the splitting lemma is no longer valid. To overcome this essential difficulty, we obtain a ground state solution directly as a minimizer on the Nehari-Pohozaev manifold by imposing a slightly stronger condition on the potentials.