Papers

Monocular 3D human pose estimation (HPE) remains challenging due to depth ambiguity, occlu- sions, and the need for temporal consistency. While multi-view methods provide superior accuracy over monocular approaches, they often require complex setups. We introduce STA-TFM, a transformer-based architecture that combines spatial and temporal information for multi-view pose estimation. The approach leverages DSTformer, a monocular feature extractor, to capture long-range pose dependencies within each view. A fusion transformer then aggregates information across views to produce coherent 3D estimates. To address training data scarcity, we use a data generation pipeline that transforms any existing 3D pose dataset into multi-view setups with controllable parameters. Experiments on various datasets demonstrate that STA-TFM outperforms existing camera-parameter-free multi-view methods. STA-TFM achieves 50.9% and 49.5% reductions in mean per joint position error (MPJPE) and mean per joint velocity error (MPJVE) on the DHP19 dataset. Furthermore, it achieves 6.7% and 7.7% respective reductions on HAA4D, and a 15.2% MPJPE reduction on TotalCapture. STA-TFM handles noisy and missing 2D inputs, supporting potential deployment in healthcare monitoring, athletic assessment, and immersive technologies. Code, training checkpoints, and data are available at https://zenodo.org/records/22832620.

We study the two-dimensional incompressible Euler-Maxwell system under the normal geometry in which the velocity and electric field are planar and the magnetic field is normal to the plane. We identify a structural distinction between the projected, charge-free formulation and the unprojected system. For the projected system, we establish a local well-posedness theory for initial velocities in $H^1(\mathbb R^2)$ with bounded initial vorticity and electromagnetic data in $H^{\frac 32}(\mathbb R^2)$, under a strict sub-luminal condition on the velocity. The main ingredient is an endpoint time-like trace estimate for half-waves, which controls the magnetic gradient in $L_t^2$ along every fluid trajectory. This closes the Yudovich vorticity estimate without requiring an Eulerian Lipschitz bound on the electromagnetic field. For the unprojected system, the longitudinal electric mode produces an additional vorticity source term containing the charge density $\operatorname{div }E$. In this case, we construct smooth, compactly supported radial electromagnetic data converging to zero in $H^{\frac32}(\mathbb R^2)$, with zero initial velocity, whose unique global smooth solution exhibits a vorticity norm inflation in $L^\infty_x$. Thus, at the same electromagnetic Sobolev regularity, the Gauss constraint separates endpoint regularity propagation from charge-driven vorticity norm inflation.

Deploying Large Language Models (LLMs) in healthcare requires robust performance across two complementary dimensions - diagnostic reasoning: the convergent, evidence-driven task of inferring a patient's condition from clinical data to produce a diagnosis, and clinical healthcare reasoning: the broader, navigational judgment required to communicate, plan, and adapt across multi-turn clinical interactions where a single correct answer may not exist. Recent benchmarks such as HealthBench and MedXpertQA reveal persistent weaknesses in both areas, exposing failures in complex diagnostic scenarios and limitations in contextual, patient-centered dialogue. We introduce a sequential training framework that targets these facets using synthetic data and rubric-based reinforcement learning. First, we improve diagnostic reasoning using MedBullets-derived questions with rule- and rubric-guided Reinforcement Learning (RL). We then shift to clinical reasoning by generating 5.3k synthetic multi-turn scenarios, each paired with multi-dimensional rubrics to comprehensively assess the response. This approach yields over 10% improvement on MedXpertQA, and our 30B model achieves 50.1% accuracy on HealthBench-Hard, surpassing proprietary baselines including GPT-5 (thinking). Our results show that targeted synthetic datasets and rubric-based training can systematically improve both diagnostic and interactive clinical reasoning in medical LLMs.

In this paper, we extend numerical schemes based on parameterized Young measures and linear programming to two space dimensions and apply them to the Kelvin-Helmholtz instability governed by the two-dimensional Euler equations of gas dynamics. We construct first-, second-, third-, fifth-, seventh-, and ninth-order Young-measure schemes and compare them with corresponding standard local Lax-Friedrichs (LLF) flux-splitting schemes and LLF schemes equipped with an entropy-based local characteristic decomposition (LLF-ELCD). We examine instantaneous and time-averaged density profiles, cumulative averages across spatial reconstruction orders, regional empirical density distributions, averaged density marginals, and several selection criteria for dissipative weak solutions. The numerical results reveal scheme-dependent flow patterns, particularly in the small-scale structures generated during the roll-up of the shear layers. At every reconstruction order considered, the Young-measure schemes yield the largest time-averaged physical entropy. By contrast, the LLF-ELCD schemes do not systematically yield larger entropy than the standard LLF schemes and therefore do not constitute a consistent maximum-entropy selection mechanism. The averaged density marginals of the Young measures are concentrated on several neighboring density states, and the later cumulative averages are closer for all Young-measure schemes. These results demonstrate the feasibility of the two-dimensional Young-measure formulation and show that the objective function in the linear-programming problem can act as an effective selection mechanism. The observed entropy preference is consistent with the local optimization of the expected physical entropy. It cannot be reproduced by merely incorporating entropy into a conventional numerical construction.

The transposition method known from the theory of second-order elliptic partial differential equations is formulated for saddle-point problems under certain structural assumptions known from the Brezzi splitting plus mapping properties that reflect elliptic regularity in concrete instances of differential operators with boundary conditions. A framework is devised that grants approximation by standard, unmodified Galerkin-type methods, which may be nonconforming with respect to the more general data allowed by the transposed operator. That the data need not be regularized is an advantage particular to the saddle-point approach. Examples covered by the framework include the Laplacian, the Stokes operator, linear elasticity, the bi-Laplacian, and the stationary Maxwell problem with $L^2$ boundary data.

Research on smartphone use remains fragmented, with studies differing in measures, methods, and platforms, limiting what we know about everyday behavior. We argue that event-level app activity logs should form the backbone of research on actual rather than recalled smartphone use. We conduct a secondary analysis of 4,571,252 app events from 1,972 participants across three longitudinal cohorts differing in age, country, recruitment, and platform, complemented by a published reference cohort. We reproduce established aggregate and micro-usage measures and examine temporal structure, application composition, transitions, and individual distinctiveness. Aggregate usage varies less than the organization of activity: adolescent use, for example, is structured around school schedules, while other cohorts show weaker within-day patterns. Application and transition patterns reveal behavioral differences obscured by screen time; an intervention reduced daily usage while increasing mean session duration. Activity traces also enabled 15-22% top-1 participant re-identification. We discuss methodological, reproducibility, and privacy implications for HCI.

Next-generation ground based gravitational wave detectors will enable precision standard-siren cosmology, making systematics increasingly important. We investigate how line-of-sight acceleration, as may arise for compact binaries in dense astrophysical environments, biases measurements of the Hubble constant $H_0$. We simulate a catalogue of 50 binary neutron star bright sirens with known host redshifts, assuming the signals have been impacted by line-of-sight acceleration and analysing them with vacuum waveforms. Unmodelled line-of-sight acceleration biases the inferred luminosity distances and shifts the individual $H_0$ posteriors systematically towards lower values. Consequently, combining events narrows the posterior around a biased value rather than averaging away the systematic, even when the acceleration signs are assigned randomly. For our 50-event catalogues, affected fractions of approximately $10\%$ at $|a_\parallel|/c=10^{-6}\,\mathrm{s^{-1}}$, or $30\%$ at $|a_\parallel|/c=10^{-7}\,\mathrm{s^{-1}}$, produce offsets exceeding three posterior standard deviations in at least one quarter of the realisations. Considering larger catalogues further increases the significance of the effect. Our results indicate that environmental effects may constitute an important systematic for precision standard-siren cosmology and should be incorporated into future population analyses.

Variational hybrid quantum models are a common paradigm for realising machine learning on quantum hardware. Nonetheless, they are challenging to train due to several problems intrinsic to the loss landscapes formed by variational quantum circuits. To mitigate these issues, researchers have extended the idea of subspace controllability leading to an increase in the success rate of variational models in finding the global minimum for quantum-based tasks. However, it remains unknown whether these results extend to classical-based tasks, and if any advantages are realised over a hyperparameter search. We begin to address this question by employing controllable circuits in a multi- classification task using MNIST-1D. Our results show that over a hyperparameter search, the majority of quantum models that achieve the lowest training and validation losses are subspace controllable. These results indicate that the hyperparameter search can be restricted to such models, in turn reducing computational cost and time.

This work investigates the use of flow-based connectivity maintenance constraints in mixed-integer linear programming (MILP) trajectory planning and decision-making models for networked multi-agent systems (MAS). We integrate flow-based encodings for standard and k-hop connectivity into MILP multi-vehicle maneuvering models that are widely used alongside receding horizon planning strategies. Their necessity and sufficiency is demonstrated, guaranteeing full coverage of potential network topologies. The flow formulation for standard connectivity decreases the growth of the required inequality constraints from exponential to polynomial w.r.t. the size of the MAS when compared to the state-of-the-art subtour elimination (SEC) method. The flow-based k-hop connectivity constraints decrease the number of required binary variables and decouple its growth from the number of hops. However, the impact of these formulations in performance is not straightforward due to the introduction of a substantial number of continuous flow optimization variables and, in the case of k-hop connectivity, additional inequality constraints. We investigate this trade-off through a statistical evaluation of costs and optimization times using a conventional branch-and-bound commercial solver and trials performed with randomized environments for increasingly larger MAS. The results show that the flow formulation outperforms SEC in standard connectivity problems, enabling the solutions to be computed for larger MAS considering the imposed optimization time limit. The reduction in number of binary variables enabled by the k-hop flow formulations decreases the theoretical worst-case number of iterations required by the branch-and-bound algorithm to compute the global optimal solution. Our results show that this advantage did not translate into improvements in the average performance when compared to the baseline.

A stochastic optimisation method was recently proposed to efficiently compute large deviation functions, used in statistical physics to characterise the fluctuations of nonequilibrium systems, modelled as Markov processes. The method, called LDSTOP, combines numerical techniques from control theory and machine learning to iteratively construct the "driven process", a controlled version of the Markov process used as a model of nonequilibrium system that realises a given fluctuation or large deviation of that system in an optimal way. Compared to other methods based on spectral approximations, importance sampling, cloning or splitting, LDSTOP is simple, flexible, and scalable, as it works by simulating single trajectories that are gradually guided towards the driven process. Here, we illustrate these advantages by applying the method on the full range of Markov processes considered in applications, namely, discrete-time Markov chains, continuous-time jump processes, and diffusion processes. For each type, we define the objective function to be optimised, explain different options available for representing the driven process (using, e.g., neural networks), and provide implementation details through simple applications. With these contributions, we aim to showcase the method's efficiency, as well as its ease of use when combined with available machine learning packages, such as PyTorch, TensorFlow and JAX, for simulating stochastic processes and solving high-dimensional optimisation problems.

We study secondary pairing in the two-flavor color-superconducting (2SC) phase, where the residual ungapped quarks form a same-chirality $J^P=1^+$ condensate driven by an attractive instanton-induced interaction. We determine its symmetry realization, quasiparticle structure, anomaly matching, and low-energy effective theory. The pairing gap is necessarily nodal; in particular, the complex axial state has two point nodes and realizes a spinful relativistic superfluid. This state preserves the full chiral symmetry ${\rm SU}(2)_{\rm L}\times{\rm SU}(2)_{\rm R}$ while breaking the modified baryon-number symmetry ${\rm U}(1)_{\tilde{\rm B}}$ and spatial rotations, with rotations about the nodal axis locked to the condensate phase. This locking gives rise to a Berry term, the Mermin-Ho relation, and a type-B orientational Nambu-Goldstone mode in addition to the superfluid phonon. We also show how anomaly matching is reorganized by secondary pairing: the perturbative mixed ${\rm SU}(2)_{\rm L,R}^2{\rm U}(1)_{\tilde{\rm B}}$ anomaly is realized by a Wess-Zumino coupling of the superfluid phonon, whereas the ${\rm SU}(2)_{\rm L}$ and ${\rm SU}(2)_{\rm R}$ Witten anomalies are carried by the point-node Bogoliubov-de Gennes flavor doublets. The resulting theory provides a concrete dense-QCD realization of a spinful relativistic superfluid with nodal fermions required by anomaly matching.

Venue prestige and citation counts are two widely used, albeit imperfect, signals of research quality. When the two signals conflict, evaluators must decide how much weight to assign each. Yet, it remains unknown how researchers across disciplines trade off these two signals when evaluating research outcome. To fill this gap, we surveyed 869 researchers using paired choices between hypothetical departmental hiring rules that assigned different weights to venue prestige and citation counts, asking which would produce better science. Among 795 respondents whose choices were largely internally consistent, choices placed nearly equal aggregate weight on the two signals. This apparent balance concealed substantial individual heterogeneity: nearly two in five respondents occupied the most venue-heavy or citation-heavy intervals. Moreover, respondents on average chose more citation-heavy rules than they believed their departments used in hiring. By revealing the subjective judgments that arise when research indicators conflict, our findings reinforce calls for greater caution when quantitative indicators are used to evaluate research.

Multimodal large language models (MLLMs) are increasingly explored as interfaces for scientific image analysis, where a visual question-answering (VQA) response may be paired with a spatial output that guides a downstream stage. A supervisor reads the language answer, while a downstream workflow such as segmentation or region review consumes the point-set output. We call this transition from inspecting the answer to relying on its point action the language-to-action hand-off. A silent failure occurs when the answer is correct while the paired action misses annotated objects needed downstream, so answer-based oversight clears a region whose action is unreliable. We introduce Spatial Action Review, a visual analytics dashboard for auditing this failure mode in electron microscopy (EM) mitochondria analysis. It links paired answer-action records through an answer-action ledger, a task-by-dataset risk map, and an image-region audit view, connecting aggregate patterns to image evidence while an adjustable action-reliability gate supports re-audit. The review ends in a human-AI hand-off, where a supervisor records whether the action is accepted, escalated, held under a stricter gate, or flagged for model revision. Across 541 image regions from an EM-adapted Qwen3-VL case-study run, point actions fail the gate in 54.4% of records with a correct VQA response, and 27.4% of all records are silent failures. A correct answer is associated with only a 5.8-percentage-point higher probability of a reliable action, with a bootstrap interval spanning zero; the point-biserial correlation between answer correctness and object coverage is 0.061. This weak coupling persists across five model conditions on 753 matched image regions. Spatial Action Review makes answer-action mismatches visible and ties them to image evidence and a recorded decision before MLLM outputs enter autonomous scientific workflows.

We study sums associated with the action of $PGL_2(\mathbb Z)$ on continuous piecewise polynomial functions with exactly two real roots, both irrational. We form weighted sums of the positive parts of their normalized transforms, using nonnegative weights compatible with translation, reflection, and inversion. Under suitable continuity, finiteness, and convergence assumptions, we prove that these sums are well defined, bounded, $1$-periodic, and continuous on $\mathbb R$, and satisfy a reciprocal functional equation. We also extend the construction to finite families of distinct function orbits. Our framework recovers Zagier's constancy result and includes the full family of quadratic sums for which Bengoechea proved convergence.

Three-dimensional (3D) multi-contrast magnetic resonance imaging (MCMRI) provides rich anatomical and quantitative information but requires long acquisition times, motivating k-space undersampling. However, reconstruction of large volumetric datasets imposes substantial computational and memory demands. To address this challenge, we propose SGAM, a memory-efficient, scan-specific framework for joint full-volume 3D MCMRI reconstruction. SGAM is based on a shared-geometry Gaussian representation in which amplitudes are modeled by a multi-output implicit neural representation (INR) and contrast-specific phases by explicit variables. This design exploits common anatomical structure across contrasts while preserving contrast-specific signal variations. The representation is jointly optimized using only the acquired multi-coil k-space without external training data. Experiments showed that SGAM consistently outperformed the comparison methods across imaging tasks and acceleration factors, with greater improvements under stronger undersampling. SGAM also achieved a favorable balance between reconstruction quality and computational cost, demonstrating its effectiveness for 3D multi-contrast MRI reconstruction.

Music festival lineups emerge from complex relationships among artists, genres, releases, labels, and past performances, making the prediction of future lineups a natural fit for temporal knowledge graph (TKG) forecasting. In this work, we present a TKG covering 380 festivals over 55 years, comprising more than 90K festival performance quadruples along with information on festivals, artist tours, and artist metadata, and release it as a resource for TKG forecasting evaluation. We formalize festival lineup forecasting as temporal link prediction between artists and festivals at future timestamps. We evaluate six TKG forecasting models on this task, analyze their capabilities and limitations, and compare them against Large Language Models applied zero-shot. Our resource complements existing TKG benchmarks by grounding evaluation in a concrete, real-world application domain.

This paper describes the design and initial evaluation of a leader-driven open collaboration platform for exploring new domains. The goal of this platform is to enable the collaboration of subject matter experts across knowledge boundaries. Traditionally, new domains are explored from within a single specialist or a focused group perspective. However, this often introduces bias. Collaboration helps reduce such bias by providing access to a broader range of information sources, increasing the chances for producing new insights in a new domain. However, it also introduces a new problem: variance between the contributions made. Variance makes it difficult to produce a coherent document. In this paper, we report on our observations from developing an initial prototype of the open collaboration platform, and derive propositions about how leader-driven open collaboration helps reduce bias while containing variance.

On a $d$-dimensional, $d\geq 2$, globally hyperbolic spacetime with a timelike boundary $(\mathcal{M},g)$, we investigate the Klein-Gordon equation with Robin boundary conditions. First of all, we prove existence and uniqueness of the advanced and retarded fundamental solutions, discussing in addition their structural properties. Secondly, under the hypothesis of infinitesimal convexity of $\partial\mathcal{M}$ and of local finiteness of boundary reflections for broken null bicharacteristics, we characterize their wavefront set in the interior $\mathring{\mathcal{M}}$, using the propagation of singularities theorem of Melrose and Sjöstrand. In the second part of the paper, we introduce a notion of Robin-Hadamard two-point correlation function as a positive distribution on $\mathcal{M}\times\mathcal{M}$ with prescribed antisymmetric part and singular structure, the latter being characterized in terms of its wavefront set. We complement this definition with a local Hadamard form. Up to a smooth remainder, this consists of the standard directed Hadamard parametrix together with additional contributions associated with the reflected null rays. Their coefficients are determined by transport equations supplemented by Robin matching conditions at the boundary. The construction applies to an arbitrary, but finite number of reflections. We prove that this local formulation is equivalent to the wavefront set condition, thereby establishing a counterpart of Radzikowski's theorem in the presence of a timelike boundary. Finally, starting from the ground state on suitable static backgrounds and using a deformation argument, we prove existence of Robin-Hadamard two-point correlation functions on the class of spacetimes considered.

Using a Large Language Model (LLM) as the clusterer at production scale is hard: prompts cannot hold the entire label space, and per-document serial processing does not deliver the throughput real workloads require. We present RAILS, a retrieval-augmented incremental LLM clusterer that turns clustering into a simple loop over a growing label pool and scales through document batching with bounded concurrency. On six public benchmarks RAILS exceeds the strongest prior LLM-clustering method on average, lifting accuracy from 51.2% to 59.3%, NMI from 67.2% to 74.8%, and ARI from 45.4% to 54.7%. We further report production-deployment evidence from a SaaS ticket-topic-discovery pipeline, where RAILS has replaced a traditional HDBSCAN stage with higher clustering quality, transparent prompt-driven control, and stateful incremental operation.

Garamvölgyi, Jordán, Király and Villányi [{Forum Math. Pi 13 (2025), Paper No.~e11}] posed two sharp connectivity conjectures for packing rigid spanning subgraphs: one for the equal-dimensional case and the other for the packing of a $d$-rigid spanning subgraph with a spanning tree. We prove a unified theorem: for arbitrary positive integers $d_1,\ldots,d_s$, every $\sum_{i=1}^{s}d_i(d_i+1)$-connected graph contains pairwise edge-disjoint spanning subgraphs $H_1,\ldots,H_s$ such that $H_i$ is $d_i$-rigid for every $i$. The connectivity bound is sharp whenever $\sum_{i=1}^{s}d_i(d_i+1)\ge4$. As special cases, the theorem settles both conjectures, confirms the conjecture of Garamvölgyi, Jordán and Király [J. Combin. Theory Ser. B 166 (2024), 1–29] that every $tk(k+1)$-connected graph contains $t$ pairwise edge-disjoint $k$-connected spanning subgraphs, and gives the sharp threshold $d(d+1)+2r$ for packing one $d$-rigid spanning subgraph together with $r$ pairwise edge-disjoint spanning trees. We also obtain two upper bounds related to Thomassen's conjecture on highly connected orientations of graphs. If $f(q)$ is the least integer such that every $f(q)$-connected graph has a $q$-connected orientation, then $f(q)\le(25q^2+41q-16)/2$ for every $q\ge3$ and $f(q)\le8q^2+212q+1404=(8+o(1))q^2$ for all sufficiently large $q$; these two results reduce the leading coefficient in the previous quadratic bound from $320$ to $25/2$ for every $q\ge3$ and $8$ for all sufficiently large $q$. Compared to the bound for $f(q)$ obtained by Garamvölgyi et al. we obtain the better bounds, not only through our tight rigidity result but also by exploiting the leftover edges when we remove two edge-disjoint spanning (sufficiently) rigid graphs.

The intermittent, stick-slip flow of amorphous systems is characterized by avalanches whose statistical properties display robust power-laws. In this paper, we study avalanche statistics in a field theoretical model of a soft-glassy system under shear. The order parameter in our model is the fluidity, which is related to the local rate of plastic events in a soft-glass. While avalanche sizes $S$ have been extensively characterized, the statistics of interevent times $t_i$ have remained largely unexplored. Here, we find that both $S$ and $t_i$ are power-law distributed and that their scaling exponents satisfy a precise relation. The model enables the analytical derivation of the scaling exponents and the reproduction of the behavior observed across a wide class of amorphous systems.

Parallel graphic processing units have been employed for fast simulations of the switching dynam- ics of Josephson junctions subject to critical current fluctuations. Such a system is modeled by a nonequilibrium washboard model with multiplicative noise, for which analytical results are lacking. The proposed approach allows us to execute extensive numerical simulation in short time and with relatively inexpensive resources. This allows us to fully characterize the effect of the noise on the junction switching current distributions at realistic bias current sweeprates.

In the classical Art Gallery Problem (AGP), guards are placed in a polygon so that together they see every point. The Witness Set Problem (WSP), introduced by Amit, Mitchell, and Packer, is a natural dual to the AGP. In this paper, we study the WSP in weak visibility polygons (WVPs), the simple polygons in which every point is seen from some point of one fixed edge. A witness set is a set of points whose visibility regions are pairwise disjoint, so that no single guard sees two of them. A maximum witness set, therefore, lower-bounds the guard number. Exact polynomial-time algorithms for the WSP are known only for monotone mountains, a proper subclass of WVPs. We give the first exact polynomial-time algorithms for the WSP in WVPs, in two settings. In the Discrete Witness Set Problem (DiscWSP), the witnesses come from a given set of $m$ points, and we find a maximum witness subset in $O(n + m \log(n+m))$ time on an $n$-vertex polygon. The algorithm rests on a structural fact: the visibility intersection graph of a WVP, in which two points are adjacent if their visibility regions intersect, is a trapezoid graph, that is, an intersection graph of trapezoids between two parallel lines. Moreover, the class of these graphs properly contains the interval graphs and the permutation graphs, which may be of independent interest in graph theory. We also prove an $\Omega(n \log n)$ lower bound in the algebraic decision-tree model for instances with $m = \Theta(n)$, so our algorithm for DiscWSP is optimum. In the Continuous Witness Set Problem (ContWSP), a witness may be any point of the polygon, and we give an exact algorithm running in $O(n \log n + \rho^{2}(n + \rho^{2}))$ time, where $\rho$ is the number of reflex vertices.

We present a first-principles study of the electronic structure and thermoelectric properties of Zn-doped SnTe using the Korringa-Kohn-Rostoker method within the coherent potential approximation, complemented by pseudopotential calculations. SnTe is a lead-free analogue of PbTe and a candidate thermoelectric material in which Zn doping has been experimentally reported to enhance the performance of $p$-type samples. We show that Zn introduces a resonant-like impurity state, located within the conduction band, which evolves strongly depending on the Zn concentration. This feature leads to a significant enhancement of the thermopower in $n$-type SnTe. In the valence band, Zn doping induces L-$\Sigma$ band convergence, also resulting in an increased $p$-type Seebeck coefficient over a broad concentration range and delaying the onset of the bipolar effect. We further demonstrate that the Zn-induced band-structure modifications drive a transition from an inverted to a trivial band ordering, indicating a controllable topological phase transition. Our results clarify the microscopic role of Zn in SnTe and identify doping as a mechanism for simultaneously tuning thermoelectric and topological properties.

We study dimension-free Riesz transform estimates on hypercubes equipped with non-uniform product measures. For $2\leq p<\infty$, we prove a dimension-free Meyer inequality for the associated carré du champ, with constants independent of both the dimension and the product measure. In contrast to the uniform case, the carré-du-champ square function does not in general coincide with the unweighted Riesz square function. Under an additional boundedness assumption on the weight parameters, we further obtain dimension-free estimates for the latter. Our proof is based on a transference from the biased hypercube to a non-tracial baby Fock model. We introduce new annihilation operators and the associated Riesz transforms on the biased hypercube, and derive explicit formulas relating them to the Riesz transforms on the non-tracial baby Fock model. The main analytic ingredient is a dimension-free $L_p$-estimate for the resulting noncommutative Riesz transform, proved by a rotation argument in the spirit of Pisier and Lust-Piquard. The same analytic mechanism also yields dimension-free Riesz transform estimates on $q$-Araki–Woods algebras.

Visualizing a chemical reaction requires making its molecular changes visible while keeping the animation faithful to the stated chemistry. Equations, structural diagrams and molecular viewers provide complementary descriptions, but assembling an interactive three-dimensional explanation still requires specifying the changes and checking their consistency. We present ChemXRG, a domain-specific language (DSL) framework that addresses this gap by representing a reaction animation as an executable program. Persistent atom identifiers and explicit bond, charge and grouping operations connect the symbolic reaction to the displayed transformation. This shared representation lets generation, verification and rendering operate on the same account of what changes. Given known, atom-mapped reactant and product structures, reaction-grounded constraints fix input-determined facts and restrict action choices; execution checks validate the resulting transformation before geometry and frames are constructed. We implement this paradigm with a reaction-program corpus and ChemQwen, a trained 0.8B DSL generator. Paired and component evaluations show improved compiler acceptance and normalized full-program agreement under input-conditioned constraints, while identifying remaining failures that require execution checks. A public browser application demonstrates the connection from symbolic reaction descriptions to inspectable programs and interactive 3D animations.

Distributed reinforcement learning (RL) scales training by parallelizing actors and learners around an Experience Buffer. As RL workloads grow, however, the buffer becomes more than a replay queue: it is the storage substrate of a large-capacity, latency-critical experience path that every iteration traverses to move, transform, sample, and batch experiences before learner updates can begin. Existing RL systems embed this path inside framework control flow or expose it as a request-driven buffer service, leaving experience placement fixed and experience-path work difficult to schedule independently as a runtime-level optimization target. We present Conduit, a framework-agnostic runtime that exposes RL experience management as an explicit systems optimization problem. At its core is the Experience Data Plane (EDP), a runtime abstraction that separates RL experience-handling semantics from framework-specific execution logic by exposing experience ingestion, experience placement, and experience delivery as explicit control points. Built on EDP, Conduit introduces capacity-constrained, bandwidth-aware placement, which distributes experience state across CPU/GPU memory tiers and nodes under heterogeneous interconnect and device-memory constraints, and latency-aware scheduling, which controls when experience-path handling runs to reduce exposed experience-path latency while preserving RL semantics. Integrated with RLlib without changing its framework execution logic, Conduit reduces exposed experience-path latency by up to 97% and end-to-end iteration latency by up to 38%, scales to 1,024 GPUs, and preserves convergence.

Intelligent transportation systems require Incremental Learning (IL) to continually improve their overall performance in dynamic environments. However, most edge devices lack the computational resources to support on-device IL, requiring updates to be transmitted from centralized servers. We propose using this setup to obtain dense, specialized module coverage that adapts a fixed base model to specific spatiotemporal contexts, such as parking lots, gas stations, ferries, or construction sites. However, in order to reliably transmit these modules to the edge device, using TCP, UDP, and BTP over V2X, Wi-Fi, and 2G-5G hardware, we establish a strict limit of 14.6 KB per module to fit within the first TCP window and to minimize UDP/BTP fragmentation. We further introduce Mixture-of-Experts for Communication-Aware Incremental Learning (MECAIL), the first method that meets this strict requirement, in which each new domain or environment is served by a small expert network that adapts the base model. We validate MECAIL on D-RICO and ODinW-13, where it largely matches the performance of parameter-heavy approaches while enabling practical, bandwidth-efficient large-scale deployment. This allows comprehensive coverage by experts for highly specific, focused, and temporary situations.

A ship starts at a point of the plane and moves at unit speed; it has to reach an unknown straight line, of which neither the distance nor the direction is known. The competitive ratio of a path is the supremum, over all lines, of the time at which the line is reached divided by its distance. Baeza-Yates, Culberson and Rawlins conjectured that a logarithmic spiral, with ratio $C_{\mathrm{sp}} = 13.8111351794611\ldots$, is optimal. We give a computer-assisted proof. Paths are arbitrary: the distance from the start and the polar angle may both decrease. The proof lifts the set of found directions to the universal cover of the circle, where unfolding the polar angle can only increase it (Kneser-Poulsen on the line); a bookkeeping inequality with a monotone final source then bounds the covered measure by the reward of a three-state relaxed control problem, in which inward motion is an ordinary control and excursions below the guaranteed disk are impulses. An explicit $C^1$ storage function, a tensor cubic B-spline plus a closed-form term, satisfies the dissipation inequalities of that problem at the spiral's level and is tight only at the spiral; this is verified with about $10^6$ boxes of Arb ball arithmetic, an exact jet and an interval Hessian at the spiral.

Predicting postprandial glycemic response (PPGR) is fundamental to personalized nutrition and type 2 diabetes management, yet existing approaches typically rely on manually reported dietary intake, limiting their scalability in free-living settings. We propose a multimodal framework that replaces manual dietary logging with image-derived macronutrient estimates and integrates them with clinical variables and gut microbiome information for personalized PPGR prediction. The framework jointly performs image-based macronutrient estimation and glucose prediction, while an attention-based prediction module models interactions between dietary and host-specific information. We evaluate the proposed approach on a real-world dataset comprising meal images, continuous glucose monitoring, clinical variables, and gut microbiome profiles. The proposed model outperforms existing PPGR baselines using image-derived nutritional inputs and approaches the performance of methods that rely on manually reported macronutrients despite using automatically estimated nutritional information. These results demonstrate that combining image-derived nutrition with complementary clinical and gut microbiome information provides a practical foundation for scalable personalized PPGR prediction.