Papers

Interactive CAPTCHAs remain challenging for computer-use agents, while existing datasets face trade-offs among type coverage, interaction fidelity, and trajectory supervision. To address these gaps, we present CaptchaArena, the first large-scale, fine-grained training dataset for interactive CAPTCHA solving. It contains 50K puzzles across 20 CAPTCHA types and 5 interaction modes, with every solution verified through execution. CaptchaArena provides 50K screenshot-action trajectories, including 46K with step-by-step reasoning annotations. It also includes fine-grained pixel-mask annotations for irregular targets. Using CaptchaArena, we train CaptchaAgent, a single 9B policy for all 20 CAPTCHA types, with supervised fine-tuning followed by reinforcement learning. The environment verifier directly provides the RL reward. Supervised fine-tuning reaches 70.5 Pass@1, and reinforcement learning further improves it to 71.7, while also improving performance on two external benchmarks. These results demonstrate the value of large-scale, fine-grained computer-use supervision for training interactive CAPTCHA agents. We release CaptchaArena and CaptchaAgent at https://github.com/X0X0X00/CaptchaArena.

The corpus-mean direction of a transformer's residual stream is a component shared across all inputs, and is commonly removed by mean-centering before representational analysis. We present evidence that it is a functional component: the reference against which the MLP gate population sets its operating point. In Phi-2, an exact decomposition of resting gate pre-activations shows that at mid-stack layers the resting inhibition of >99.9% of gates is carried by the coupling $w \cdot b_L$ to the carried mean direction, at 48-56$\times$ the explicit bias parameter, and the coupling is direction-specific: a random direction at matched norm orders the population's firing rates at Spearman $\rho \leq 0.09$ where the reference reaches 0.95. (That 0.95 is near-tautological on its own; the paper derives its null.) Causally, removing the stream's projection on the reference multiplies above-threshold firing by about 9$\times$, dose-monotonically, at 23-59$\times$ a norm-matched control; a random-initialised twin is flat, and replacement tests show that the direction carries the function and the magnitude does not. A direction-matched control makes the same point: noise injected along the reference costs 8-42$\times$ the same energy along a random direction. The decomposition replicates on four further families spanning both gate types (GELU with an explicit gate bias, bias-free SwiGLU), and the dose-response on two of them. Across an eight-model scan the mechanism is present in every GELU and SiLU family and absent only in OPT, where an opposing LayerNorm bias cancels the carried reference. Gate thresholds are implemented as couplings to a constant the network builds for the distribution it is reading, with the bias parameters contributing little; how much of that constant is carried in the stream and how much in parameters depends on the architecture.

Single-cell time-lapse microscopy now provides high-resolution size trajectories for thousands of individual cells, yet principled methods for simultaneously learning the functional form of growth laws and the distribution of cell-to-cell physiological variability remain limited. We present a data-driven framework based on the recent Weak-form Estimation of Nonlinear Dynamics (WENDy) algorithm to (i) select the best supported growth law from a set of candidate laws, and (ii) recover individual-level growth parameters via empirical Bayes shrinkage within a random-effects model. We demonstrate the approach on both synthetic individual size data incorporating commonly found growth laws and recorded real size trajectories, showing that the method accurately recovers both growth-law structure and parameter heterogeneity at reasonable noise levels. We finally end with a discussion on how the results obtained by the method here can be upscaled to the population level.

In this paper, we provide a construction of an acyclic discrete vector field that is compatible with a total order associated with a lower star filtration on a simplicial complex, called the colex vector field. We show that the colex vector field induces a filtered acyclic vector field, whose resulting Morse complex computes the persistent homology of the lower star filtration on the underlying simplicial complex. We show that the colex vector field can be recomputed quickly when the vertex function that induces the lower star filtration is modified via order-adjacent vertex swaps. We provide a framework for storing and computing the number of paths between cells in the simplicial complex, as well as a method to update these values quickly when the colex vector field changes. Finally, we provide publicly available proof-of-concept code for the ideas shown. When applying it to the Persistent Homology Transform, we show that its runtime is comparable to a more standard matrix reduction approach.

We study density of states (DOS) estimation for large sparse real symmetric matrices by fitting the cumulative density of states (CDOS) and differentiating the fit. We use a stochastic Lanczos method to supply Ritz values and weights, which we average across Lanczos runs to construct CDOS midpoint data. Monotone piecewise-cubic interpolation of these data yields a smooth CDOS approximation that can be easily differentiated to yield a nonnegative, normalized, piecewise-quadratic DOS without requiring a Gaussian smoothing with a fixed bandwidth in its construction. We also consider approximating CDOS by using Gaussian-process regression (GPR) with single- and double-Gaussian covariance kernels, yielding an approximation with uncertainty information. DOS approximation is then obtained by analytic derivative of the GPR-based CDOS. Experiments on matrices from diverse scientific applications are performed to compare these estimators with Gaussian-broadened stochastic Lanczos and Jackson-damped kernel polynomial approximations. At a common Gaussian validation resolution, we use error measures that assess local discrepancies, integrated errors, and agreement in the overall spectral shape. The results demonstrate that the midpoint spline can produce accurate approximations to the DOS with relatively few matrix–vector products, supporting the use of cumulative interpolation as a practical DOS estimation.

A point-defect cavity side-coupled to a line-defect waveguide in a two-dimensional photonic crystal of silicon rods in water is studied with plane-wave expansion and finite-difference time-domain computations. The defect-rod radius tunes the resonance continuously within the band gap, as first-order perturbation theory predicts, whereas the quality factor changes in discrete steps set by the number of lattice rows between cavity and guide; displacing the defect rod by up to a tenth of a period changes it by less than 7 percent. Each added row multiplies the quality factor by a factor that follows, without an adjustable parameter, from the decay of the evanescent Bloch channel of the bulk crystal that is phase-matched to the guided mode; the channel at zero wavevector along the guide predicts little more than half that factor. Two biases of a finite computational domain, leakage across the cladding and a standing wave set up by reflections at the ends of the truncated guide, lower the per-row factor and change the quality factor by up to a factor of two if left uncorrected. Scaled to 1550 nm the design gives a sensitivity of 634 nm per refractive index unit, which perturbation theory reproduces, and the linewidth agrees with that of a transmission spectrum normalized to a cavity-free reference. Absorption by water caps the quality factor near 9200 and limits the useful number of barrier rows. The guided mode lies inside the light cone, so a slab of finite height needs a different guide.

Many economic decisions rely on observations that predate the decision time. This paper introduces information latency, the elapsed time between a decision and the most recent observation of an evolving payoff-relevant state, as a distinct source of imperfect information. Unlike classical sources of information friction, latency generates irreducible uncertainty even with exact observations and rational expectations. For sufficiently regular continuous-time Markov processes, conditional variance increases locally with latency; under the Ornstein-Uhlenbeck benchmark, it increases at a decreasing rate toward a finite bound. Following a rare-state observation, however, uncertainty can peak at an intermediate latency before declining. Neither the average latency nor the average update frequency fully characterizes information quality: the regularity of information arrival matters independently of the mean interval. Under a CARA-normal benchmark, latency-induced uncertainty generates a risk premium. With heterogeneous latency, the lowest-risk-adjusted-cost intermediary wins the business, while competition drives the price toward the second-lowest risk-adjusted cost. In a stylized contract-renewal setting, positive latency can be second-best optimal by limiting costly reclassification when direct contractual commitment is unavailable. The framework applies to credit, insurance, financial markets, and operational decisions.

Quantitative measurement of nanoscale stray magnetic fields during domain reversal is important for understanding and optimizing magnetic memory and logic devices. Yet, achieving high spatial resolution with minimally invasive probes remains challenging. Here we demonstrate nanodiamonds (NDs) hosting an ensemble nitrogen vacancy (NV) centers as local quantum sensors of domain-reversal stray fields in a CoFeB strip. During magnetic-field-driven reversal, the ND sensors resolve three distinct local responses depending on their positions relative to the strip: a positive frequency jump at the edge, an unexpected negative jump just outside the strip, and a negligible change near the center. These contrasting signals are quantitatively explained by magnetostatic boundary fields from micromagnetic simulations. We further implement a fully constrained fitting procedure for optically detected magnetic resonance spectra, enabling robust field extraction even when resonances are partially resolved. Together, these results establish NV-ND magnetometry as a simple, transferable, and quantitative approach for characterizing spatially heterogeneous magnetic fields in thin-films and spintronic devices.

We show that, on the Fourier side, the sharp second order Heisenberg Uncertainty Principle (HUP) and its sharp stability for functions are nothing but the first order $L^{2}$-Caffarelli–Kohn–Nirenberg inequality and its sharp stability, applied to their Fourier transforms. This gives a proof in a few lines of the sharp stability estimate that we established recently by a much longer argument. The same observation then produces two one-parameter families of sharp fractional Heisenberg Uncertainty Principles, in which the gradient is replaced by a fractional power of the Laplacian: for each of them we compute the sharp constants, characterize all the optimizers, and establish the sharp stability estimates. The stability constant of the first family is equal to $1$ for every nonnegative order and every dimension. Negative orders, where the fractional Laplacian becomes a Riesz potential, are treated as well. Finally, we show that the deficit carries much more information than the distance to the optimizers alone: it controls an explicit chain of successive remainder terms whose constants are the successive spectral gaps of an explicit operator. For the classical Heisenberg Uncertainty Principle this gives three remainder terms with optimal explicit constants, and for the second order HUP a chain of four remainder terms measured against explicit confluent hypergeometric profiles and coupled through one single set of parameters. As applications, we also establish the chain of stability of the HUP for curl-free vector fields.

Real-time full-duplex speech models can listen while speaking, enabling natural interaction without rigid turn boundaries. Existing benchmarks evaluate turn-taking, interruption handling and multi-round dialogue, but largely centre on a designated user rather than an assistant participating in a shared conversation among several people. We introduce Duplex-MPE to evaluate when such an assistant should answer, remain silent or stop speaking. The benchmark contains 2,000 scenarios with three or four human speakers and one assistant, each paired across explicit and implicit addressing of the same request. Models receive continuous conversation audio without transcripts or supplied turn boundaries. Four scores measure fresh response initiation, answer accuracy, silence preservation and stopping when a human resolves a request. We evaluate eight open-weight speech systems: MiniCPM-o 4.5, Moshi, FLM-Audio, Voila, Freeze-Omni, Realtime-Venus-Audio, Moshika-RL-Seamless and PersonaPlex. MiniCPM-o 4.5 leads on three scored capabilities, while frequent speech from other systems can coexist with inaccurate answers or failures to remain silent. A transcript-based Gemini 3.1 Pro reference responds 64.3 percentage points more often to explicit than implicit requests; paired tests detect no significant response-presence difference for the speech systems.

Hybrid transformer architectures that replace most softmax attention layers with linear attention offer transformer-level quality at a fraction of the memory cost. Rather than pretraining such models, a growing body of work distills them from already trained full-attention transformers. However, these distilled models often collapse on long-context retrieval and reasoning tasks, particularly when operating in thinking mode, where the efficiency gains of hybrid architectures matter most. Since linear attention layers must compress context into a fixed-size state, their errors compound over long sequences. As off-policy distillation never teaches the student model to recover from this drift, tasks that necessitate longer sequence lengths become especially challenging. We introduce On-Policy Attention Linearization (OPAL) in which the hybrid attention student samples its own long-context trajectories and receives dense supervision from the frozen full-attention teacher. Applying OPAL to Qwen3-4B and MiMo-7B-RL-0530, we recover $87$–$94\%$ of full-attention performance on commonsense reasoning, $100\%$ on needle-in-a-haystack (NIAH) retrieval, and $83$–$93\%$ on mathematical reasoning with only 3B training tokens. We achieve these results without supervised fine-tuning (SFT) or reinforcement learning with verifiable rewards (RLVR). Compared with the strongest prior linearization method, which recovers $68\%$ of its teacher's retrieval performance and $21.6\%$ absolute average mathematical reasoning accuracy, OPAL fully recovers retrieval and achieves $67.6$–$72.2\%$ on math reasoning.

We present a neural method for adaptive triangle mesh refinement, in which an autoregressive model adds geometric detail to selected regions of an input mesh while leaving the rest unchanged, a key capability for efficiently allocating mesh budget. Existing upsampling methods struggle to achieve this. Classical subdivision schemes refine triangulation without semantic awareness of the underlying shape or the ability to recover geometric details missing from a coarse input. Recent neural mesh models generate shapes globally, sacrificing region-specific control. We propose a novel tokenizer that yields combinatorially many valid upsampling trajectories from a single mesh. Trained on such data, our locally-conditioned autoregressive architecture allows for direct manipulation of topology and geometry within target regions of an input mesh. We validate our method against state-of-the-art approaches and demonstrate its ability to perform adaptive upsampling with region-selective control, a capability absent from existing approaches. This unlocks inference-time view-dependent refinement, physics-aware region refinement, and coarse-shape conditioned novel mesh synthesis. We provide code at https://github.com/seanxzhan/learned-localized-mesh-refinement/.

We consider a McKean-Vlasov equation incorporating spatial fast oscillatory behavior into both the energetic and kinematic components of the model. The former is given in terms of a confining potential while the latter by an underlying metric. The equation is formulated as a gradient flow in the space of probability measures endowed with a Wasserstein metric. We identify the limiting dynamics which is also described as a gradient flow in an effective media. We further prove the long time exponential convergence of solutions to the invariant measure. The rate of convergence is expressed in terms of a Logarithmic Sobolev constant which is uniform in terms of the oscillatory length scale. Our approach is based on variational and functional inequalities. The homogenization result of the current paper extends the authors' previous work [GaoYip] on a linear Fokker-Planck equation to a nonlinear and nonlocal setting.

We present a new strong-lensing and X-ray mass model of the merging galaxy cluster SPT-CLJ1150-2805 ($z=0.383$), combining JWST NIRCam, HST, Chandra, and VLT/MUSE data to robustly decompose its collisionless and collisional components. Exploiting JWST, we expand the multiple-image catalogue with 66 new images (30 comprising 6 new systems). Our baseline model uses 118 spectroscopically confirmed images from 20 systems, achieving an image-plane root-mean-square offset of $0.56''$. An expanded model incorporating 31 additional photometric images from 8 additional systems yields a near-identical mass distribution, confirming excellent model stability. We resolve a complex multi-axis post-merger system requiring five cluster-scale dark matter haloes, including a bimodal core with distinct haloes coincident with each brightest cluster galaxy. The remaining mass components are independently supported by kinematics of 291 cluster members ($\sigma_v=1960^{+84}_{-92}$ km s$^{-1}$), which reveal two new galaxy substructures - the northernmost of which we tentatively identify as the baryonic counterpart to our fifth dark matter halo. The cluster is an extraordinarily efficient lens, possessing an effective Einstein radius $\theta_E=42.41^{+0.05}_{-0.04}{''}$ and an enclosed mass $M(<\theta_E)=3.35^{+0.04}_{-0.03}\times10^{14}M_\odot$ for a source at $z_s=2$. For a high-redshift source at $z_s=9$, it produces a magnification cross-section of $A(>10)\simeq0.15$ arcmin$^2$ and $A(>30)\simeq0.020$ arcmin$^2$. This global lensing power surpasses all Hubble Frontier Fields clusters. In a regime where systematic uncertainties between mass models dominate high-redshift magnification errors, the stability of our reconstruction sets this lens apart. This combination of extreme lensing power and a robust mass model establishes SPT-CLJ1150-2805 as a premier cosmic telescope for high-redshift studies.

The origins of strong magnetic fields observed in many white dwarfs are uncertain. Recent observations show that such fields are more common for white dwarfs with crystallized cores. Crystallization creates a destabilizing composition gradient that drives thermohaline convection in the star's fluid envelope, which may play an important role in magnetic field emergence. We perform 3D magnetohydrodynamical simulations of thermohaline convection with magnetic fields of various strengths and orientations, using the Boussinesq approximation in periodic Cartesian boxes. Our simulations suggest that thermohaline convection can generate magnetic fields when the magnetic Prandtl number is large (i.e., low magnetic diffusivity), but they are likely too weak to account for those observed in magnetic white dwarfs. However, the simulations indicate that strong magnetic fields can be advected outwards by the thermohaline convection without being destroyed, depending on the net magnetic flux. Hence, crystallization-induced thermohaline mixing may transport magnetic fields initially trapped in white dwarf interiors to their outer layers, allowing them to be observed. However, additional simulations using more realistic geometry and magnetic field configurations will be needed to confirm this possibility.

Broadband lasers suppress the absolute two-plasmon-decay instability that preheats inertial-fusion targets. The usual scaling relates this suppression to the drive's coherence time, a power-spectrum statistic insensitive to spectral phase. By gradient descent through a differentiable enveloped wave solver, we show that at fixed power spectrum phase optimization raises the threshold from the random-phase median of $2.8\,I_\mathrm{mono}$ to $4.1\,I_\mathrm{mono}$, but produces a transform-limited (TL) pulse train with peak-to-average ratio $R=32$. Joint amplitude–phase optimization reaches $5.6\,I_\mathrm{mono}$ at $R=3.6$, above the best tested TL line-count result of $4.5\,I_\mathrm{mono}$ at $R=16$; relaxing the peak constraint raises the joint threshold to $6.4\,I_\mathrm{mono}$. An exact growth-rate budget evaluated inside the simulation separates the two mechanisms. TL suppresses coupling mainly by concentrating the pump field into short bursts, thereby lowering its time-averaged magnitude at fixed average intensity. The joint optima retain near-random values of this amplitude measure while suppressing both the available coupling and the fraction realized through pump–daughter alignment. The advantage of joint optimization persists from $1\%$ to $4\%$ bandwidth and from OMEGA-scale to ignition-scale conditions.

This engineering study assesses gaze-assisted data acquisition during visual screening with a Gaze Quest implementation via webcam and GC308 near infrared camera with an Orlosky eye tracking pipeline. Ten subjects performed under both acquisition conditions. Accuracy of Tumbling E orientation, reported application logMAR value,and response latency were determined from keyboard responses and hence are behavioral outputs as opposed toeye tracker screening results. Frame-to-frame change in theangle between successive normalized gaze vectors (28.2degrees) served as the GC308 eye tracker derived diagnostic with an effective sampling rate of roughly 8 FPS. No screen target calibration or gaze to screen translation was done on the GC308 eye tracker output data for the current analysis and hence, these data represent acquisition stability and not gaze accuracy in relation to the target. The webcam pipeline relied on 25-point screen calibration. Because the display resolution and pixel pitch could not be retained in the records of the study, the reported application logMAR values cannot be viewed as measures of visual acuity in any way.

Multi-objective Bayesian optimization (MOBO) is commonly approached through specialized acquisition functions or scalarization schemes designed to explicitly account for trade-offs among non-preferential objectives. In this work, we show that such complexity might be unnecessary. We propose a framework that extends standard single-objective acquisition functions directly to the multi-objective setting through a hypervolume-based methodology. We further extend hedge strategies for acquisition functions, which are typically used only in single-objective optimization, to the multi-objective regime. Our approach requires minimal modification to existing Bayesian optimization pipelines and avoids the need for bespoke multi-objective formulations. We demonstrate how a broad class of commonly used single-objective acquisition functions and hedge strategies can be adapted in a principled manner to handle multiple objectives, while preserving their intuitive interpretation and computational efficiency. Empirically, we evaluate the proposed methods across a range of synthetic and real-world multi-objective benchmarks. Despite their simplicity, our extensions consistently match or outperform more complex state-of-the-art MOBO methods in terms of optimization performance and sample efficiency. These results suggest that effective multi-objective Bayesian optimization can be achieved by reusing and carefully extending well-established single-objective acquisition strategies, offering a simpler and more flexible alternative to existing approaches.

Agentic biomedical machine learning (ML) draws on complementary advances in biomedical evidence acquisition and executable program search. Existing systems connect aspects of these capabilities, but coordinating them throughout program search remains challenging. New evidence must guide candidate construction, execution outcomes must inform subsequent discovery and reuse, and validation demands must fit the search budget. We introduce BioDyad, which couples biomedical discovery and ML engineering through two hierarchies within Monte Carlo graph search. Its scientific hierarchy combines prior biomedical guidance with iterative discovery, then links biomedical plans to execution outcomes in memory for reuse across candidates. Its engineering hierarchy moves candidate programs from smoke execution, through train/validation evaluation, to full-data retraining. We evaluate BioDyad on the 76-task BioXArena benchmark under a two-hour per-task budget with three matched LLM backends. It achieves the highest penalized all-task score and task success rate among four agent methods and a one-shot baseline under each backend. These results support coordinating biomedical discovery and ML engineering to integrate external knowledge into executable programs across heterogeneous biomedical tasks.

Generative world models can provide visual rollouts for embodied planning, yet their feasibility on edge devices depends not only on the learned model but also on how the execution runtime represents its operations. We introduce a cache-aware lowering that expresses supported causal Conv3D calls as batched spatial Conv2D operations while preserving pretrained weights, temporal-cache semantics, convolution parameters, bias placement, and output layout. Across the complete Cosmos3-Edge image-to-video pipeline on a 64-GB NVIDIA Jetson AGX Orin, the proposed route accelerates VAE decoding by approximately $7\times$ and reduces complete-generation latency by more than $2\times$, while repeated decoder evaluations maintain complete fast-path coverage without fallbacks. The unchanged lowering also improves Cosmos3-Nano and transfers to LingBot-World's architecturally distinct Wan2.1 VAE. A clean-device comparison against fully specialized TensorRT shows that TensorRT provides a further $1.36\times$ steady-state improvement, but requires substantially greater per-module and per-runtime-state AOT specialization. Same-latent BF16 and FP32 evaluations characterize the finite-precision differences introduced by the alternative execution order. Together, these results position cache-aware lowering as a lightweight runtime optimization that recovers most of the available decoder acceleration without modifying the learned models themselves.

Large language model (LLM) agents built on the ReAct pattern concentrate four responsibilities in one model: selecting a strategy, choosing each action, formatting it, and judging whether the result is adequate. Nothing outside the generative loop can reject its output, so an agent that cannot progress does not report failure; it runs until an external budget terminates it. We propose VReAct, which treats verification as an architectural layer for ReAct agents by adapting the software-engineering V-model: specification levels descend from requirements to individual steps, each paired with a dedicated verifier; a deterministic controller enforces every verdict; and only verification outcomes write memory. A rejection thus localizes the level that introduced the fault, and an agent halts by declining rather than by exhaustion. Each verifier separates a zero-cost deterministic gate from an optional LLM judge, so the contribution and cost of each can be measured independently. A pilot study implements the acceptance- and unit-level verifier pairs, comparing five configurations that share one executor, tool set, and scorer and differ only in verification components, on the four-hop stratum of MuSiQue with an 8B-parameter backbone. Across 47 executions, the two unverified configurations answered none of ten questions, every run ending at a step cap or provider token limit; the verified configuration without a planner answered eight of ten and abstained on the rest. Deterministic gates produced eight of nine observed corrections at zero marginal cost, and planning degraded performance once verification was present. These results characterize termination behavior, not accuracy at scale; we outline a twelve-month plan to complete and evaluate the full architecture, including the integration-level pair the pilot omits.

We present Potential-Dominant Operator Splitting (PDO-Split), a real-time generalized Nash equilibrium solver for constrained dynamic multi-agent problems with potential-dominant structure. PDO-Split targets the computational bottleneck in game-theoretic model predictive control, where repeatedly solving the equilibrium KKT system becomes costly as the number of agents increases. We introduce a class of gamma-potential-dominant games, in which the potential (or cooperative) structure dominates the competitive interactions between the agents. We show that this structure allows PDO-Split to use the potential component as a preconditioner while incorporating the competitive component through iterative refinement. We establish convergence guarantees and exploit the symmetry of the potential component through a reusable LDL^T factorization to accelerate the linear solvers. We evaluate PDO-Split across several practical multi-agent planning problems, including eight-car racing and six-vehicle ramp merging, achieving substantially improved runtime and convergence rate over existing DDP-based and Newton-based methods, especially with a larger number of agents. The algorithm is also experimentally validated on miniature autonomous race car platforms, demonstrating the approach's real-time capability.

In forensic science, when crime-scene evidence (CSE) and suspect-related evidence (SRE) is present, it is customary to report on the value of this evidence in the form of a likelihood ratio (LR). The LR can be calculated as the probability of CSE given SRE divided by the probability of CSE given that it was generated by a randomly selected person from an alternative culprit population. In forensic science, this is known as a feature-based LR, and intuitively the LR contrasts "similarity" by "typicality". Since it is generally a problem for feature-based LRs to find appropriate models for the data, one either resorts to score-based LRs or to adjusting the feature-based output post-hoc to well-calibrated output. Either way, the above definition of the LR is broken and interpretation of the LR as similarity between CSE and SRE divided by typicality of CSE is destroyed. Here, we report on progress in obtaining instantly well-performing feature-based LRs using gradient descent in combination with Bayesian probability theory to train a two-level model, the main LR model in forensic science for describing distributions of continuous data. For a dataset of laser-ablation inductively-coupled-plasma mass-spectrometry measurements on glass fragments from forensic casework, we show that our best model on validation data yields much better calibrated feature-based LRs on the test set when compared to state-of-the-art feature-based LR systems trained on the same type of data, and that it improves a factor of 4.5 on average on $C_{\mathrm{llr}}$. For LRs interpretable in terms of "similarity" contrasting "typicality", this is a major advancement. However, a state-of-the-art LR system still performs a factor of 1.5 better on $C_{\mathrm{llr}}$ for this data. We also present future plans to close this remaining gap. In order to facilitate collaboration, we have put relevant code on GitHub.

Overcoming experimental errors is a central challenge in quantum science. This challenge is particularly acute in large and complex quantum circuits, where quantum information spreads into exponentially many paths, foiling any direct attempt to understand errors' impact. In this work, we present a novel approach to understanding and mitigating experimental errors, based on a surprisingly compact representation of a quantum circuit's information dynamics, the reactivity function. The shape of a circuit's reactivity function governs its noise response, and its amenability to different error mitigation methods. From this viewpoint, we introduce two complementary such methods. The first, Pauli-path zero-noise extrapolation, fits a parameterized model to a circuit's reactivity function and uses it to accurately extrapolate to zero noise. The second, tunable error cancellation, filters a circuit's reactivity function to cancel noise on all information up to a threshold locality. Crucially, both methods feature a tuning parameter that allows one to systematically improve their accuracy until convergence. Across three circuit families from published experiments, our methods overcome conventional zero-noise extrapolation biases as large as 30%; at $\sim$$10^{-2}$ root-mean-square error, they reduce sampling cost relative to probabilistic error cancellation by up to a factor of $10^3$.

Native-latent guidance is a recent paradigm for solving inverse problems with latent diffusion models. It replaces repeated evaluations of the image-space forward model, each requiring a decoder pass, with efficient guidance computed using a learned latent-space surrogate. However, existing methods apply guidance uniformly across latent dimensions, ignoring that measurements are informative only along certain directions and that the reliability of model predictions varies across inputs and timesteps. We propose ANaLOG, a framework for efficient uncertainty-aware guidance with pretrained latent diffusion models. ANaLOG models uncertainty by learning an anisotropic, input- and time-dependent covariance that is integrated into the guidance mechanism to emphasize reliable directions and downweight uncertain ones. We theoretically analyze this framework in a linear model setting and prove that anisotropic, uncertainty-aware weighting is necessary for correct sampling, whereas isotropic guidance induces sampling errors. Experiments across five challenging inverse problems show that ANaLOG improves perceptual reconstruction quality over existing methods while preserving efficiency.

Low-Earth-orbit (LEO) satellites are increasingly expected to perform onboard learning for applications such as disaster response and environmental monitoring. However, conventional federated learning (FL) is ill-suited to onboard satellite learning, as it assumes computational, memory, and communication resources beyond the capabilities of resource-constrained LEO platforms, often necessitating the transmission of raw imagery to ground stations. We present COSMIC-FL, a resource-aware FL framework for efficient onboard learning in LEO satellite constellations. COSMIC-FL introduces two complementary Mixture-of-Experts (MoE) architectures: a Sliced design that shares backbone representations while activating task-specific channel subsets, and a Modular design that employs lightweight gating to route inputs to physically separated expert networks. A semantic class-to-expert mapping enables each satellite to train, update, and communicate only the expert paths relevant to its local data. To further improve efficiency, COSMIC-FL integrates staged optimization with three structured pruning strategies: server-side pruning, client-side fixed-ratio pruning with mean-vote aggregation, and adaptive client-side per-layer pruning based on aggregated importance and a MAD-based gap criterion. Combined with semantic expert routing, these techniques jointly adapt computation and model sparsity to both data semantics and layer importance, yielding a favourable accuracy–efficiency trade-off for heterogeneous space platforms. Experiments on six image classification benchmarks under highly non-i.i.d. settings show that COSMIC-FL maintains competitive accuracy while reducing communication, computation, and energy consumption by up to 80% over SOTA FL methods. We further validate COSMIC-FL on an NVIDIA Jetson AGX Orin, confirming its efficiency gains under realistic embedded deployment constraints.

Random forests (RF) are tree-based models that capture complex, high-order predictor interactions. In biomedical studies, ordered outcomes often have outliers, skewness, or mixtures of continuous and ordinal values (e.g., due to detection limits). Standard RF splitting targets conditional means via squared errors and is sensitive to such irregularities. We propose a Wilcoxon regression tree that selects splits by maximizing a rank-based impurity reduction, equivalent to maximizing the squared Wilcoxon rank-sum statistic. Because the criterion depends only on outcome ranks, it is invariant to monotone transformations and naturally accommodates continuous, ordinal, or mixed outcomes. We develop the Wilcoxon random forest (WRF), which aggregates Wilcoxon regression trees via subsampling and estimates conditional distributions using forest-weighted empirical CDFs. We establish consistency of the WRF distribution estimator under regularity conditions. We evaluate distributional prediction using calibration diagnostics and continuous ranked probability scores, and define an out-of-bag permutation variable-importance measure. Simulations show that the WRF performs comparably to the standard quantile regression forest when errors are symmetric and homoscedastic, and yields improved quantile estimation and calibration when outcomes are skewed or heteroscedastic. We apply the WRF to predict CD4 cell count and HIV viral load six months after antiretroviral therapy initiation in a multicenter Latin American cohort, and the WRF improves threshold probability estimation and accommodates the large mass at the viral load detection limit.

The Tangent Galvanometer (TG) is a standard undergraduate laboratory experiment for estimating the horizontal component of Earth's magnetic field (BH) by measuring the angle of deflection of a magnetic needle corresponding to the current flowing through a circular coil. In this study, an artificial neural network (ANN) is used as a complementary data-driven model to predict the value of BH. A dataset comprising 225 observations obtained using 50-turn and 500-turn coils was used for developing the ANN model. After quality control, 223 observations were retained and divided into training (70%), validation (15%), and testing (15%) subsets. The model was optimized using a feed-forward neural network with Tanh activation. Three different models (Models A, B, and C) with different input variables were compared for optimum performance. Model C used five input variables: current, deflection angle, tan(theta), magnetic field produced by the coil, and number of turns. The addition of tan(theta) produced a substantial improvement in prediction performance, which was further improved by including the magnetic field produced by the coil. Model C gave the best test performance, with R2 = 0.99053, RMSE = 0.54076 microT, and MAE = 0.32940 microT. The experimental and ANN-predicted values of BH were also compared with an adopted local geomagnetic reference value of 39.0 microT. The mean experimental and ANN-predicted values were 37.38898 microT and 37.32161 microT, respectively. The results demonstrate the usefulness of ANN as a complementary tool for analyzing experimental variability and nonlinear relationships in an undergraduate physics laboratory experiment.

Newton methods efficiently find Generalized Nash Equilibria (GNE) in dynamic games by solving for the KKT necessary conditions. These methods are fast and can support multi-agent Model Predictive Control (MPC) for highly dynamic robots. However, a small KKT residual alone does not certify that the returned solution satisfies the second-order sufficient conditions for a local GNE. In this paper, we propose an efficient numerical method to verify the second-order sufficient conditions (SOSC) for a local GNE. We connect the inertia of the agent KKT matrix with the positive definiteness of the reduced Hessian of the cost function, projected onto the null space of the constraints. Furthermore, we introduce an inertia-corrected update step that improves convergence to local GNEs by destabilizing strict saddle points with weak cross-agent coupling. Our main contribution is a fast Newton solver for Constrained Dynamic Games that provides efficient optimality checking. Through numerical benchmarks, we demonstrate the proposed solver's runtime and convergence performance in practical multi-agent planning problems. We also validate the solver's real-time capabilities in physical experiments using a platform of miniature autonomous race cars.

In this thesis, we consider general relativity on a manifold with a timelike boundary of finite size, across all signs of the cosmological constant $\Lambda$. We impose conformal boundary conditions, whereby the conformal class of the induced metric and the trace of the extrinsic curvature $K$ are fixed at the boundary. In Lorentzian signature, we analyse the linearised Einstein equations about Minkowski, de Sitter (dS), and anti-de Sitter (AdS) space for a variety of boundaries, employing the Kodama-Ishibashi formalism adapted to manifolds with a boundary. In Euclidean signature, we study the thermodynamics of black hole and cosmological horizons enclosed by the boundary, computing the leading semiclassical approximation of the gravitational path integral, for which the boundary data define a conformal canonical ensemble of fixed conformal temperature and $K$.