Papers

We develop a sequential ensemble MCMC scheme for Bayesian pulsar timing and noise analysis that uses data size as the tempering parameter. The method enables gradual and reliable convergence from potentially uninformed initial points by iteratively increasing the data size, thereby increasing sensitivity and progressively narrowing the target distribution until the posterior of the full dataset is reached. The initial iterations use sub-datasets that can be orders of magnitude smaller than the full dataset, substantially reducing computational cost, which is further lowered by employing approximate lower-rank models justified by the reduced sensitivity of these sub-datasets. Bayesian inference is performed using the final MCMC chain sampled from the true target distribution after applying appropriate burn-in. We demonstrate the method using the NANOGrav 12.5-year data of PSR B1855+09, showing progressive convergence to the target posterior and that most of the computational time is spent sampling the true target distribution rather than in the preceding tempered iterations.

A compressor can keep the facts of a dialogue and still drop the turn that changed them. A user corrects a price, reverses a choice, or adds a constraint. We call this failure turning-point eviction. One overall retention score hides it, because that score mixes what the user first wanted with what the user wants now. We introduce TPBench, which evaluates three complementary information targets at shared nominal retention budgets. P1 asks for the user's initial goal. P2 asks for the current value of a slot the user revised. P3 asks for both, in dialogues with a late annotated slot update. The current-value answers come from the human dialogue-state annotations of MultiWOZ and SGD. The initial-goal answer is the first sentence of the first user turn. Neither requires new crowdsourcing. The probe-specific evaluations rank compression methods differently. On the joint probe at a retained fraction of 0.30, every tested compressed method remains below full context with the main Llama reader. Deleting the turn that carries the update sharply lowers current-value accuracy, while deleting one matched irrelevant turn leaves it unchanged. A Mistral reader repeats the P2/P3 rankings and the joint-probe gap. Current-value recovery is tested on an additional corpus, LongMemEval-KU, and on Chinese RiSAWOZ: full context has the highest accuracy, and recency has the highest compressed-method mean in both evaluations.

Motivated by searches for weak primordial non-Gaussianity in the cosmic microwave background, we investigate perturbative departures from Gaussian stochastic gravitational wave background statistics using pulsar timing arrays. We consider a quadratic ansatz that shows three-point correlations at first order in the nonlinear coupling and covariance corrections at second order. We first examine the ansatz for gravitational wave helicity amplitudes. However, the timing residual bispectrum that this produces is not manifestly invariant under local polarization basis rotations for tensor and vector modes. Then, we formulate a polarization-frame-invariant phenomenological model for detector-projected amplitudes and evaluate its one-pulsar timing residual third moment with a simplified response. Our numerical benchmarks have shown that this gives a very small Gaussian-rms-normalized skewness.

Hyperedge faults remain a major challenge in circuit-level quantum error correction. Accurately exploiting hyperedge correlations often requires substantial computational resources, which complicates real-time decoding. Matching-based decoders are fast and scalable, but their pairwise graph representation limits the use of higher-order fault information. Here, we introduce Syndrome Motif Projection (SMP), a general framework for incorporating hyperedge information into matching-based decoding. The key idea is that a hyperedge fault produces a characteristic local syndrome motif. Observing such a motif provides evidence for the corresponding fault. SMP extracts this information directly from the measured syndrome with linear-complexity preprocessing while preserving the matching backend. It can therefore serve as a lightweight front end to existing scalable and real-time matching decoders. We demonstrate SMP across surface code memories, color code memories, and logical gate circuits. On Google's Willow experimental surface code data, SMP improves both standard and correlated matching and outperforms the tested belief matching baseline. For color code memories, SMP combined with Chromobius reduces logical failure probabilities by up to 77.8%. For logical gate circuits, SMP reduces the failure probability of a six-CNOT circuit by 35.5% relative to logical observable matching while achieving performance comparable to iterative belief matching. These results demonstrate that SMP provides a lightweight and transferable approach to hyperedge decoding, with a clear path toward integration into scalable real-time decoding architectures for fault-tolerant quantum computation.

Wave-energy relation is introduced as a new analysis tool for linear radial pulsations. Wave energy consists of kinetic energy, acoustic-potential energy, dynamical-potential energy, and entropy-potential energy. The relation describes changes in the wave energy caused by non-adiabatic processes and by leakage of wave energy. It is applied to modal analysis of adiabatic pulsations for the massive Zero Age Main Sequence models (10, 20, and 30 solar masses). The ordinary modes are well trapped in the interior cavity without any significant wave-energy leakage. On the other hand, the strange modes (S-modes) exhibit the steep increases in the eigenfunctions and kinetic energy toward the stellar surface and the significant wave-energy leakage. The kinetic energy of S-modes is no longer confined in the exterior cavity.

Evaluating distributed LLM serving designs on physical clusters is costly. Yet existing simulators provide only subsets of the capabilities needed for realistic design exploration: stateful closed-loop execution, timing prediction without profiling target hardware, and direct execution of unmodified serving benchmarks. We present ServeTwin, a closed-loop simulator that couples specification-driven analytical timing with a stateful serving loop. This coupling captures feedback among request completion, scheduling, queue state, and KV-cache evolution, including prefill-decode disaggregation and multi-turn agent workloads. ServeTwin avoids target-hardware operator profiling through iSTAGE, an analytical trace generator that derives per-iteration traces from model and engine specifications while representing ragged batches and discrete engine mechanisms such as CUDA-graph batch padding. It further decomposes execution time into component-owned throughput, scheduler, and runtime costs. This ownership lets unaffected parameters transfer across platforms and confines recalibration to changed hardware or software components. ServeTwin implements a vLLM-compatible interface and runs unmodified serving benchmarks. Against real deployments, it reproduces InferenceX's steady-state throughput-interactivity frontier with a 3.6% mean error and predicts LMBenchmark's multi-turn performance with a 9.9% error while tracking KV-cache evolution. Pre-silicon sweeps reveal that the preferred HBM bandwidth-capacity tradeoff reverses across workload states and that increasing concurrency shifts the bottleneck from memory bandwidth to scheduler and runtime overheads. Together, these capabilities enable practical exploration of distributed LLM serving systems before target hardware is available.

Generative AI weakens the link between assessed performance and the cognitive processes that educational work is expected to reflect. This paper examines observable traces of those processes in a sample of 150 student-AI conversations. The analysis uses the concept of epistemic ownership as an interpretive framework, focusing on three dimensions that can become visible in interaction: Direction, Integration, and Evaluation. The results show that similar assessed performance can coexist with substantially different observable patterns of cognitive participation. Assignment scores therefore provide information about assessed outcomes but do not recover how cognitive work was distributed between student and AI during the interaction. The study provides an empirical basis for asking how assessment should incorporate evidence about cognitive process, rather than relying exclusively on the quality of the resulting product.

This paper proposes a new functional approximation approach to reduce Bellman error in high-dimensional dynamic programming and Reinforcement Learning problems. Using a classic dynamic programming problem (network capacity control in revenue management) as the motivational example, the paper illustrates that deep neural networks and linear programming approximation algorithms can be combined to derive approximate solutions to dynamic programming problems. Simulation results show the proposed approximation algorithms achieves competitive performance when compared with benchmark.

Of the two black holes, M87$^\ast$ and Sgr~A$^\ast$, for which event-horizon-scale imaging is currently achievable, only Sgr~A$^\ast$ at our Galactic Center exhibits sub-hour variability, making light curve observations of the inner accretion flow especially valuable for time-domain studies of the spacetime and the surrounding plasma. Observed light curves are often sampled with variable cadence, so a structure function is often used to quantify their variability properties. In this work, we assemble a heterogeneous Sgr~A$^\ast$ light curve data set from discrete observations acquired over $\sim12$ years at 230 GHz, with different instruments, durations, and cadences, and study its structure function in three frameworks. First, we consider analytic predictions for the features of structure functions of stationary random processes with Fourier spectra dictated by the Matérn covariance. We then study the structure functions resulting from lensed movies of synthetic optically thin accretion flows approximated with Matérn covariance in both space and time, and identify which features in the structure function can be attributed to the black-hole geometry. Lastly, we examine the structure functions of a library of $72$ general relativistic magnetohydrodynamic simulations. We find that, in general, magnetically arrested disk (MAD) models produce smoother structure functions with steeper slopes than standard and normal evolution (SANE) counterparts. On time scales of $5-15$ minutes, the observed structure function slope of Sgr~A$^\ast$ more closely aligns with the MAD trend, while both simulation types are generally more variable than the data on all sub-hour timescales.

Closed-loop learned locomotion is established on commercial quadrupeds but remains uncommon at the sub-kilogram scale. Continuous-rotation legs give MiNI-Q, a 270 g quadruped, access to supporting configurations on either side of the body. We exploit this range with a single posture-conditioned reinforcement-learning policy that runs entirely onboard. A continuous joint-space reference on the torus $T^8$ and its gravity-conditioned transformation connect upright walking, inverted walking, and landing recovery without state machines or phase switching. Coordinated posture and release curricula train this behavior family; identified actuation, cross-engine validation, and embedded execution support hardware transfer. The same sub-100k-parameter network tracks forward velocity with RMSE of 0.037 m/s upright and 0.050 m/s inverted, resumes walking in 24 of 30 release trials, and operates with four interchangeable foot geometries across four indoor surfaces. Hardware experiments and simulation ablations connect these capabilities to the representation, conditioning, and training choices that exploit the platform's motion range. Demonstration videos and supplementary material are available on the project website: https://submissionreview.github.io/around-the-world/.

In this paper, we study favorite sites of one-dimensional transient random walk on $\mathbb{Z}$ beyond the simple case. Denote by $\mathcal{K}(n)$ the set of favorite sites at time $n$. The goal of this paper is twofold. First, we study $\# \mathcal{K}(n)$, the cardinality of $\mathcal{K}(n)$, and show that, under some mild conditions, for any positive integer $k$, $\mathbf{P}(\#\mathcal{K}(n)=k, {\rm i.o.})=1$, and $\limsup_{n\to\infty}\#\mathcal{K}(n)/\log\log n=-1/\log \gamma$, where $\gamma$ is the probability that the random walk never returns to the starting point. Second, we study the escape rate of favorite sites, and give the limsup and liminf behaviors, where the liminf behavior is characterized via an integral test. To the best of our knowledge, this integral test is the first result of this nature for random walks (in non-random environments).

Flow-matching-based multi-view world models generate realistic videos, but are commonly restricted to fixed camera rigs. Extending them to continuously varying camera poses requires paired pose–video observations with dense pose coverage, which are costly to acquire. We introduce SymRegFlow, a symmetry-regularized flow-matching framework for multi-view-consistent video generation across continuous viewpoints without ground-truth novel-view RGB supervision. For each target pose, SymRegFlow geometrically warps source views into noisy anchors and combines masked dual-anchor supervision with cross-anchor denoising-output consistency to mitigate anchor-specific errors. Under an affine Gaussian surrogate, we prove that suitable consistency regularization recovers the clean-reference optimum at fixed noise levels, strictly outperforming single- and merged-anchor baselines. Experiments on Cosmos-Drive-Dreams and nuScenes demonstrate high-quality, multi-view-consistent autonomous-driving video generation: on nuScenes, SymRegFlow achieves the lowest FVD and FVMD among the evaluated baselines, reducing FVD by over 31% relative to the best baseline, and source-conditioned inference also attains the best FID and instance preservation.

Strong well-filteredness is a refinement of well-filteredness arising naturally in non-Hausdorff topology and domain theory. In this paper, we construct a countable locally compact strong R-space X such that neither its Smyth power space nor its Scott power space is a strong d-space. This example gives negative answers to the questions concerning the preservation of strong well-filteredness and the strong R-space property under power space constructions. Furthermore, for the two-point discrete space \two, the function space (\two,X) is not a strong d-space under any of the pointwise convergence, compact-open, Isbell, core-open or Scott topologies, where the Scott topology is induced by the pointwise order.

Rates of convergence in normal approximation are fundamental to probability and statistics. The theory has evolved from normalized sums to Studentized statistics, smooth functions of sample means, and $U$-statistics, and more generally to symmetric statistics. A central question throughout this development has been to identify the weakest assumptions under which optimal rates of convergence can be established. First, in this paper we address this question by establishing optimal bounds for adjusted normal approximations of symmetric statistics based on independent and identically distributed observations. More precisely, we bound the Kolmogorov error by a very neat sum of the classical third-moment term and the variance of the remainder term. This resolves a long-standing conjecture posed by Bentkus, Jing and Zhou (Ann. Probab. 37 (2009), 2174–2199). Secondly, we establish the optimal Berry-Esseen rate for jackknife Studentized \(U\)-statistics of order two under minimal conditions, i.e., a finite third absolute moment of the first projection and a finite \(5/3\)-absolute moment of the canonical kernel. This resolves a long-standing conjecture in classical probability theory. Our proofs combine signed Prawitz smoothing with a conditional-variance submartingale, polynomial approximation, and a bounded change of measure.

A flag complex $L$ determines a locally CAT(0) cube complex $P_L$ with the links of all vertices isomorphic to $L$. The fundamental group of $P_L$ is the commutator subgroup of the right-angled Coxeter group $W_L$. We observe that an edge contraction $L \rightarrow L/e$ determines a $2$-fold branched cover $P_L \rightarrow P_{L/e}$ (up to a homotopy equivalence). We use this branched cover to give an inequality between the $\mathbb{F}_2$-$L^2$-Betti numbers of $W_L$ and $W_{L/e}$. This reduces an $\mathbb{F}_2$-version of the Singer Conjecture for right-angled Coxeter groups to minimal flag triangulations of even dimensional spheres. We also use this inequality to compute the $L^2$-Betti numbers of $W_L$ when $L$ is a flag triangulation of the projective plane or the torus.

Structural connectivity (SC) and functional connectivity (FC) provide complementary information on interactions between brain regions and are widely used in neuroimaging studies of neuropsychiatric disorders. Generative modelling can alleviate the scarcity of large-scale paired SC-FC data, but existing approaches typically use pairwise graphs that capture only dyadic interactions and often generate SC and FC independently, limiting preservation of higher-order structure-function relationships. We propose a Multimodal Hypergraph Flow Matching (MHG-FM) framework for joint SC-FC connectivity generation and cross-modal translation. MHG-FM constructs modality-specific hypergraphs, learns higher-order representations with Hypergraph Neural Network (HGNN) encoders, and performs bidirectional cross-modal fusion using Dual Cross-Attention (DCA). A variational autoencoder maps the fused representations to a compact latent space, where conditional flow matching enables connectivity synthesis and multimodal translation via latent transport. Experiments on the Human Connectome Project Young Adult (HCP-YA) dataset show that MHG-FM outperforms several state-of-the-art baselines in reconstruction quality, topology preservation, distributional similarity, and SC-FC coupling, while achieving approximately 8x faster sampling than a matched diffusion backbone.

We study large-data continuation below the critical energy for the two-dimensional sphere-valued Schrödinger map \[ \partial_t u=u\times\Delta u, \qquad u:[0,T_+)\times\mathbb{R}^2\to\mathbb{S}^2, \qquad E(u_0)<4\pi. \] Working directly with the original equation through the complex tangential fields $W_m=\partial_m u+\mathrm{i} u\times\partial_m u$ and the ambient connections $\Gamma_\alpha$, we prove frequency-envelope bounds governed by the critical norm $\|\nabla u\|_{\ell^2L^4_{t,x}}$. As consequences, $T_+=\infty$ if $\|\nabla u\|_{\ell^2L^4([0,T_+)\times\mathbb{R}^2)}<\infty$, and also if a terminal one-window high-frequency tail $\mathcal{A}_{\mathrm{win}}(t)$ satisfies $\liminf_{t\uparrow T_+}\mathcal{A}_{\mathrm{win}}(t)<\varepsilon_*$. Thus any finite-time failure must force persistent high-frequency concentration on all sufficiently late critical parabolic windows.

Growing volumes of educational real-world data (ERWD) are being collected across learning platforms and institutional systems. Sharing these data within the Learning Analytics community offers substantial research opportunities, yet access remains limited by ethical, regulatory and governance constraints. Prior work has primarily focused on anonymisation techniques, but little attention has been paid to operational design of practical ERWD sharing, particularly how data custodians and researchers interact through privacy-preserving access mechanisms. To address this gap, we propose ReLEAF, a socio-technical framework that bridges data custodians and researchers by operationalising two-stage data sharing: 1) Differentially private synthetic data are shared for exploratory analysis, and 2) controlled real-data validation is performed on demand. Following a design-science research approach, we refine and formatively evaluate ReLEAF through three cycles involving 4 graduate students, 6 researchers, and 90 undergraduate students, respectively. Three design principles emerged through the cycles: P1) position privacy-preserving access mechanisms within the research workflow, P2) make the conditions for acceptable secondary use explicit and actionable, and P3) promote engagement with governance requirements rather than automate compliance decisions. Together, ReLEAF provides a concrete framework for trustworthy ERWD sharing, while the design principles offer transferable guidance for other data-sharing contexts.

Power-system synchronization studies mainly ask whether synchronization can be achieved, whereas a complementary question is how well post-disturbance synchronization recovery can be shaped. In inverter-dominated systems, this recovery involves coupled phase-angle and voltage-magnitude dynamics, for which complex frequency provides a unified representation. This paper establishes a conservation law for synchronization recovery in this representation. For a given system and its initial state, the logarithmic integral of the proposed recovery residual is fixed by the initial contraction rate and the right-half-plane (RHP) zero–pole structure. Hence, synchronization recovery performance cannot be improved uniformly over frequencies and variables unless the budget set by these terms changes; controller tuning that preserves them can only redistribute the residual response across frequencies. The conservation law applies to both linear and nonlinear recovery responses satisfying the mild analyticity conditions. It further yields finite-frequency peak–bandwidth limits and a lower bound on the time-domain integral of squared complex frequency recovery. A system-level extension recovers classical Bode-type sensitivity conservation as an LTI special case. Studies on a heterogeneous IEEE 39-bus system verify the theory.

Vision-language models such as CLIP exhibit strong semantic generalization, but remain limited in fine-grained visual perception. A recent work named KUEA presents a natural remedy by finetuning the image encoder under the supervision of the vision-centric DINOv2 to align their kernel matrices element-wisely, while regularizing the embeddings to remain close to the pretrained visual encoder for preserving image-text semantics in CLIP. However, we show that diminishing the role of the alignment loss to DINOv2 does not necessarily degrade its fine-grained visual performance, suggesting that the kernel-matrix discrepancy may be insufficient for further visual representation enhancement, motivating us to revisit the alignment formulation. In this work, we present a novel perspective to characterize representation alignment on feature subspaces through Kernel Canonical Correlation Analysis (KCCA), which maximizes the projection correlations. In optimization, we derive an efficient end-to-end training scheme upon KKT conditions, avoiding the eigenvalue problem in KCCA. Further, we extend our method into a 3-view formulation, i.e., 3vKCCA, in which the projections from the pretrained text encoder are also incorporated under a unified optimization framework for joint alignment. With CLIP ViT-L/14 on ImageNet-1K, our 3vKCCA improves the MMVP-VLM accuracy from 17.8 to 25.9, substantially outperforming the existing methods, and meanwhile maintains zero-shot image–text retrieval performance.

A key challenge in bringing embodied intelligence into the real world is transferring capabilities from simulation to reality and enabling agents to continually adapt after deployment. End-to-end vision-language-action policies provide strong manipulation capabilities, but their transfer to physical environments typically relies on calibrating simulated visual and dynamical conditions, collecting additional target-domain demonstrations, and optimizing the policy through further training. Tool-using embodied agents offer flexible task orchestration, yet existing systems primarily emphasize task execution and experience reuse within a given environment, with limited support for transferring procedural knowledge and continuously adapting it across simulation and reality. We propose RoboBridge, a framework that treats sim-to-real transfer as the continued adaptation of executable task skills. The agent represents task knowledge as procedures connecting task intent, observations, tool operations, and outcome verification. Interaction feedback is used to generate candidate skill revisions, which are evaluated before being persisted or rejected. A pretrained vision-language-action policy is exposed as a reusable action tool and enhanced with inference-time guidance, enabling fine-grained execution without retraining the underlying policy. RoboBridge grounds transferable skills in task semantics and interaction interfaces shared across simulation and reality. This representation preserves reusable task structure while allowing environment-dependent operations to be selectively revised through real-world execution feedback. We evaluate the framework on LIBERO-PRO and corresponding physical tasks, studying both skill evolution and post-transfer adaptation. Our framework provides a route from one-shot policy deployment to continual procedural learning across environments.

Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer. We study the finite computation obtained by releasing the $N$-th iterate of deterministic gradient descent on $w\mapsto F(w;S)+\langle z,w\rangle$, where $z\sim\mathcal N(0,\sigma^2I_d)$ is drawn once before optimization. For strongly convex and smooth objectives with Lipschitz Hessian, we prove an explicit condition under which the map $z\mapsto w_N$ is a $C^1$-diffeomorphism on the bounded domains used in the privacy argument, with a quantitative lower bound on the smallest singular value of its Jacobian. This permits a direct change-of-variables analysis of the finite iterate. For generalized linear models, the resulting privacy-profile bound has no explicit ambient-dimension factor once the iteration condition holds, and its finite-iteration correction decreases geometrically. By letting the free truncation parameter grow slowly with $N$, we recover the corresponding exact-minimizer certificate in the limit. We also bound the expected excess empirical risk by $d\sigma^2/(2\mu)$ plus a geometrically decreasing optimization term, and transfer the result to population risk without an additional multiplicative condition-number factor in the leading statistical terms.

Egocentric videos capture how people carry out everyday activities, yet testing an agent requires evaluating the consequences of actions it chooses itself. We introduce Ego2World, a benchmark that turns annotated cooking activities into executable planning environments under partial observation. Its compiler links source steps and objects to symbolic action rules, persistent world states, and explicit task conditions, so researchers can execute an agent's proposed actions and check their outcomes. World state and agent belief are maintained separately, enabling controlled studies of planning and information reuse across continuing tasks. Evaluating six planners on 105 tasks shows that accepted operations often leave task goals unmet. Execution traces and condition checks distinguish interrupted runs, partial attainment, and completed execution without goal attainment. In a separate paired Qwen-Plus study, persistent belief improves action validity by 4.15 percentage points and reduces visual-query attempts by 90.27%, with higher token use and no detected completion gain. Ego2World provides a reusable testbed for tracing how planning and memory choices affect execution, observation demand, and task attainment, connecting recorded human activity to the development and evaluation of interactive agents.

This paper studies finite-terminal continuation and subthreshold global existence for the two-dimensional Landau–Lifshitz–Gilbert equation in the $H_Q^2$ strong-solution class. The proof shows that if a maximal strong solution terminates at a finite time and the full-frequency $L^4_{t,x}$ norm of $\nabla u$ is finite on a terminal time window, then the strong solution can be continued. Furthermore, the solution can still be continued as long as the ultraviolet tail above one fixed dyadic cutoff belongs to $L^4_{t,x}$. As applications, we obtain global strong solutions when $E(u_0)<4\pi$; in the degree-zero sector, this energy threshold can be raised to $8\pi$.

Most KV-cache compression methods classify attention heads once, either offline or during prefill, and keep this classification fixed throughout generation. Across three models (1.5B-8B) and three regimes (needle retrieval, long chain-of-thought, and multi-turn recall), we measure head behavior on four model-regime combinations and find that most heads change their reading behavior at least once during generation. We introduce WakeKV, a reactive residency policy that moves cooling heads to a recoverable CPU reservoir rather than freezing or permanently evicting their state. At matched memory or budget, WakeKV consistently improves miss rate over frozen classification and destructive eviction, evaluated across five model-regime combinations and over three cited baselines (SnapKV, uniform R-KV, and ReasonAlloc) across four eligible combinations. A FlexiCache/vLLM implementation on Mistral-7B confirms the benefit on real hardware, improving throughput while retaining LongBench quality.

In the photoreceptor compass model, a light-generated, spin-correlated radical pair undergoes singlet-triplet interconversion driven by Zeeman and anisotropic hyperfine interactions, leading to orientation-dependent reaction yields. In this study, we consider simultaneously the spin environment and the boson environment surrounding the radical-pair system and concentrate on the correlated memory effect of the spin bath. In the linear-response limit, the spin bath is mapped to an effective Gaussian environment. The system dynamics and yields under its influence together with the bosonic bath are propagated uniformly using the hierarchical equations of motion (HEOM) or equivalently the dissipaton equations of motion (DEOM) method. The HEOM/DEOM is non-Markovian and non-perturbative, exact for Gaussian environments. Corresponding results of the Markovian Lindblad master equation are also shown for comparison. Numerical demonstrations highlight the non-Markovian memory effect as a crucial ingredient for radical-pair magnetoreception.

Human activity recognition (HAR) from wrist-worn accelerometers is increasingly used for health and behavioral tracking. Yet, most wearable HAR models are developed and evaluated on datasets dominated by younger adults, leaving it unclear whether benchmark progress generalizes across age groups. In this work, we leverage MyMove, our carefully annotated, free-living older-adult HAR dataset (mean age 71), to evaluate deep-learning architectures and training regimes under both leave-one-subject-out and cross-dataset transfer. We find that improvements on younger-adult benchmarks fail to transfer equally to data collected from older adults, resulting in a persistent and often widening performance gap. However, richer representations, particularly frozen self-supervised features pretrained on the age-diverse UK Biobank dataset, substantially improve performance on data from older adults and consistently narrow the performance gap, at modest cost to younger-adult performance, though disparities remain. These findings suggest that benchmark gains and architectural scaling alone provide an incomplete picture of progress in wearable HAR, and broader advances may require representations that better capture population diversity, alongside personalized adaptation to individual movement patterns and routines.

Terminal agents are increasingly deployed beyond software engineering in science and other specialized domains. Constructing training environments requires executable reference behavior and a domain-specific verifier that distinguishes semantic correctness from superficially plausible artifacts. Authoring these components for each task requires repeated engineering and limits reuse. We introduce software-in-the-loop reconstruction, a self-supervised framework that obtains reference outputs and verification targets from existing software workflows, executable programs mapping structured inputs to outputs. For each workflow, we execute multiple input configurations and partition cases into public observations and hidden evaluations. Given the instruction, input schema, and public input–output observations, an agent constructs an editable program without access to the source workflow. The candidate is evaluated on hidden configurations against workflow outputs. A hierarchical verifier combines domain-specific semantic comparison, structural validity, and anti-shortcut checks, while public feedback supports iterative revision. The construction admits additional workflows and configurations without authoring a reference solution for each task. We instantiate SWR with 500 workflows and 46 software families across six domains. Across three attempts per task, Qwen3.8-Max solves 838 tasks and produces 1,422 verified trajectories, which we oversample to 3,000 reconstruction-only training examples. Supervised fine-tuning of Qwen3.8-27B improves mean Terminal-Bench 2 performance from 47.94% to 53.56% across three seeds and achieves the highest mean among four matched-token corpus controls on all four reported evaluations. These results indicate that existing scientific software can provide scalable, behaviorally verified supervision for terminal agents.

In this paper, we obtain extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than that from Soundararajan's classical resonance method. Consequently, we show that one branch of the dichotomy established by Bondarenko, Darbar, Hagen, Heap, and Seip (2023) can be realized for this family of Dirichlet $L$-functions. The proof relies on the resonance method together with precise estimates for GCD sums.

Wet-lab experimentation serves as the gold standard for hypothesis verification in scientific discovery; yet it is inherently labor-intensive, costly, and safety-critical. Embodied agents hold the promise of automating these tedious workflows, but their development is hindered by the scarcity of real-world training data. While simulation offers a scalable alternative for producing demonstrations, current methods primarily target relatively short-horizon tasks with loosely structured interactions, failing to meet the strict procedural constraints and fine-grained manipulation demands of chemical experiments. To bridge this gap, we introduce RoboChemGym, a framework that autonomously generates high-fidelity manipulation demonstrations aligned with real-world experiment protocols, featuring a self-improving task synthesis mechanism to iteratively refine task execution and scene configurations, enabling the reliable generation of expert trajectories for complex, multi-object protocols exceeding 10 interaction steps. Furthermore, we introduce a hierarchical benchmark that systematically assesses performance across varying granularities, spanning from atomic operations to full-cycle experimental workflows. RoboChemGym sets a scalable paradigm for the automated data synthesis and capability evaluation of embodied agents in intricate chemical tasks, serving as a critical stepping stone toward fully intelligent laboratories.