Papers

True random number generators (TRNGs) based on the dark noise of perimeter-gated single-photon avalanche diodes (pg-SPADs) naturally produce outputs that follow a tunable Bernoulli distribution. For applications requiring non-uniform random numbers, multiple such units can be coupled, or the inherent Poisson statistics of the accumulated dark events from a single pg-SPAD can be exploited. In this work, we present the principles for extending pg-SPAD-based TRNGs from the uniform to the non-uniform regime and investigate the impact of the perimeter-gate voltage on the underlying probability distributions. The proposed concepts were experimentally validated using a prototype 64 x 64 pg-SPAD chip, fabricated in a standard 0.35 $\mu$m CMOS process. Collectively, we showed that common non-uniform distributions such as Poisson, exponential, and approximated Gaussian can be achieved and tuned in real-time using pg-SPAD TRNGs.

Research on large language model agents for penetration testing is evaluated almost entirely by capability: whether the agent captures a flag or reproduces a proof of concept. That metric suits a benchmark but is silent on the properties that decide whether an autonomous agent can be used in an authorized engagement: whether a reported finding is true, whether the agent stayed inside its authorized scope, and whether an operator can audit what it did. We call these assurance properties and argue that they belong to the harness, the runtime wrapping the model, and can be enforced in code. This paper makes three contributions. First, we define a framework of five assurance properties (evidence grounding, non destructive claim reduction, computed severity, enforced authorization, and tamper evident accountability), each with a formal model and an explicit acceptance test, connected to prior work in capability based security, tamper evident logging, and software provenance. Second, we position representative systems (PentestGPT, the Cochise reference harness, MAPTA, and the trajectory judge PentestJudge) within the framework using published coding criteria, and identify a consistent assurance gap. Third, we study one open source implementation, NeuroSploit, pinned to an exact commit, reporting its architecture, its complexity cost, and a content addressed artifact bundle from a run against a public deliberately vulnerable target. We execute the deterministic authorization and audit acceptance tests directly and find and report a real enforcement gap, which we reflect by scoring both properties as partial. We therefore claim an initial existence argument that the properties are realizable together, not a comparative performance result, and we specify the multi target, ablation, and adversarial evaluation protocol required to turn the framework obligations into measurements.

Molecular systems have many degrees of freedom, but their metastable behavior can often be described by a few collective variables. Identifying these variables and estimating free energies along them from limited simulation data remains a challenging, important problem. Separate short trajectories may sample different metastable states without capturing transitions or establishing their relative equilibrium populations. For unbiased trajectories generated with the same Hamiltonian at a single temperature, alternate methods based on histogram reweighting cannot correct this imbalance. Here we present SPIBER, which combines the State Predictive Information Bottleneck (SPIB) with Generative Flow Networks (GFlowNets). SPIB uses deep learning to approximate slow degrees of freedom through a past-future information bottleneck, retaining information needed to predict future metastable states. We show that this compression limits conditional entropy variations in populated regions, allowing conditional mean potential energies, which are much easier to calculate, to be used to approximate free energy differences. Given sufficient local sampling to estimate these energies, they define the target distribution for GFlowNets, energy-based generative samplers that sample according to estimated thermodynamic stability rather than observed populations. For a particle in a radial double-well potential, for alanine dipeptide, and for the nine-residue peptide AIB9, SPIBER recovers free energy differences between sampled metastable states to within one thermal energy unit of reference values. The method combines collective-variable learning and free energy estimation in up to four latent dimensions, without requiring converged state populations or additional molecular dynamics simulations.

In neutrino scattering experiments, the emitted final state particles are essential for identifying interaction channels and reconstructing neutrino energies. During intranuclear propagation, neutrino-induced hadrons can interact with surrounding nucleons, altering both the number of final state particles and detectable energy depositions. As a result, neutrino experiments rely on hadron-nucleus scattering models to simulate these nuclear effects. This paper explores nucleon production predicted by hadron scattering models for common hadrons in neutrino experiments, specifically nucleons and pions. We investigate these models with simulations from the GENIE neutrino event generator, which includes implementations of Geant4 Bertini Cascade and INCL++. For popular target nuclei, we find that the number of emitted nucleons for mesonless hadron interactions can be parameterized by simple Gaussian and exponential decay functions. We present these relationships and provide reweighting tools for addressing the hadron scattering model spread in both visible energy and final state nucleon multiplicities.

Nitrogen-vacancy (NV) centers have emerged as a highly sensitive platform for spatially resolved temperature measurements. When the $\lvert0\rangle\to\lvert+1\rangle$ and $\lvert0\rangle\to\lvert-1\rangle$ transitions are nearly degenerate and the Rabi frequency is comparable to the transition splitting, the spin dynamics encountered during pulsed protocols for temperature measurement can significantly alter the intended accumulation of temperature-dependent phase. We investigate these triplet ($\lvert0\rangle$, $\lvert\pm1\rangle$) spin dynamics and their effect on pulsed thermometry protocols under these conditions. We find that the conventional thermal-echo timing produces negligible temperature-sensitive signal amplitudes at the common-mode detuning. However, we find that the nominal spin-echo timing produces resolvable oscillations at the common-mode detuning, leading to a strong temperature-sensitive carrier signal. This departure from the expected protocol behavior is qualitatively captured by an ensemble model of the triplet dynamics, which supports significant dark-state leakage as a plausible mechanism for the temperature-sensitive response. This mixing-enabled thermal echo uses a four-phase quadrature readout that resolves the signed oscillation frequency and is validated using independent sweeps of the microwave carrier frequency and fluid temperature. We further assess the ability of a four-refocusing-pulse (LDD4B) low-field dynamical-decoupling sequence to extend the NV coherence and find that while the echo retains a sensitivity to common-mode detuning, the effective phase-accumulation interval corresponds to approximately half the total evolution time. These findings could support the use of pulsed NV thermometry in biological or mobile applications where applying magnetic bias fields is impractical and microwave power may be limited.

Recent work has shown that, if a large fraction of the LIGO-Virgo-KAGRA compact binary coalescences (CBCs) occur in accretion disks around active galactic nuclei (AGNs), many such AGN-CBC systems will likely experience lensing and produce multiple gravitational-wave (GW) "images" of the CBCs that will become detectable with current or future GW detectors. However, the waveforms produced by such lensed "images" will differ from those produced by other lensing systems because the binary source is orbiting the AGN's central supermassive black hole at a close distance. Here, we show that these systems produce 2 snapshots of the same binary source from 2 different viewing angles. These differences in the effective viewing angle between the images are encoded in the GWs they emit, such that GW detectors can effectively analyse the waveforms from 2 viewpoints. Beyond such "multi-view lensing", the GW images may also differ by their Doppler shift due to the expected relativistic orbital motion of the source around the AGN, an effect which is further amplified by the proximity to the lens. If the AGN's own angular momentum can be related to the binary's orbital angular momentum, we can describe the entire AGN-CBC system using only one additional free parameter compared with a typical point-mass lens system, or with 3 additional parameters when we do not make such an assumption. In this work, we establish a framework of transformation rules that describe both the angles in the 2 points of view, and the Doppler effect that comes from the source's motion around the lens. We also provide the framework to produce consistent AGN-lensed waveforms from any currently available GW waveform. These AGN-CBC systems give 2 unique points of view on a binary merger thus opening up a new window into the merger's properties unlike any other lens system.

We study the log-concavity property of first Dirichlet eigenfunctions on domains in $\mathbb{CP}^2$. For every smooth $1$-convex domain $\Omega\subset\mathbb{CP}^2$, we prove the quantitative estimate \[ \nabla^2(-\log u) > \max\left\{\psi(s),\frac85\right\}g, \text{ where } \psi(|\grad f|^2) = \frac{s}{\sqrt{1+s}}-\log(1+s), \] for its first Dirichlet eigenfunction $u$. In particular, $u$ is strictly log-concave. As consequences, we obtain a uniform convexity estimate for the regular level sets of $u$ and the fundamental gap bound $\lambda_2-\lambda_1>46/5$.

Implanted neurostimulators that sense local field potentials now enable chronic electrophysiology based biomarker tracking in patients at home. The Medtronic Percept PC, the only commercially available sensing-enabled deep brain stimulation (DBS) device, stores spectral amplitudes as 16-bit integers at approximately 0.1 $\mu$V per bit (quantum $q \approx 0.11$ $\mu$Vp). At frequencies where the true amplitude spans only a few quantization levels, consecutive bins round to the same stored value. Standard spectral parameterization (FOOOF, fitting oscillations and one over f), which separates periodic peaks from the aperiodic 1/f activity, treats every value as exact and fits oscillatory peaks to these plateaus. Because these spectra feed clinical biomarker pipelines and spectral foundation models for symptom decoding, spurious peaks can corrupt downstream inference. Across 9,438 spectra from 14 hemispheres in 7 subcallosal cingulate DBS patients, 20.6% of peaks detected at [2, 45] Hz have no match in ground truth synthesized by quantizing clean in-clinic BrainSense recordings, while aggregate beta band power and the aperiodic exponent are preserved. We formalize dequantization as interval-censored subspace estimation and compare five classes of correction methods. Quantized probabilistic PCA is the only tested method that reduces the spurious rate (20.6% to 18.3%) while preserving true peak detection and keeping noise floor RMSE below $q/\sqrt{12}$.

We address a problem concerning cinema audiences: “A cinema has $n$ seats numbered from $1$ to $n$, and there are $n$ people with tickets numbered from $1$ to $n$. People enter the cinema in order. If someone has the ticket number $i$, they can choose seats whose numbers are multiples of $i$. They should exit the cinema if the permitted seats are occupied by previous audience members. In how many ways can they be seated under these conditions?" We give an algorithm to create the list of situations that meet these conditions. We also focus on finding the number of situations in two special cases: when exactly one seat is unoccupied whose total number is denoted by $\omega(n)$, and when all audiences $1, \ldots, n-1$ are seated, whose total number is denoted by $\psi(n)$. Giving the recursive formula $\psi(n)=1+\sum_{d|n, d\neq n}\psi(d)$ with the initial value $\psi(1)=1$, we provide an explicit formula for $\psi(p^\alpha q^\beta)$, where $p$ and $q$ are distinct prime numbers. Furthermore, we show that $\omega(n)=-n+\sum_{i=1}^n\psi(i)$.

The linearized buckling load of a stiffened panel depends on the stress stiffness its shell element assembles. We read it from exported operators against three truncations of one second variation. The classic pass of ANSYS SHELL181 carries a rotation-rotation block pairing the drilling freedom with the bending rotations and its perturbation pass does not; removing the block recovers the perturbation load factor to 0.02%. SHELL281 carries block and couplings in both passes. Abaqus S4 matches the critical mode of the complete second variation to 1.0000 on the translations and its load factor to 1.7%, against 17% and 34% for the other two forms. On an optimized panel under cantilevered shear a 20-node continuum lies 3% to 6% above that form, S4 and SHELL281, 11% and 23% below both SHELL181 passes and 25% above Abaqus S8R, at the finest meshes. On a conventionally stiffened panel the SHELL181 passes stand 1.0% and 3.5% above the complete form, 9% and 21% at half the rib pitch; under a shear flow, on cylinders, open beams and under axial compression the three forms coincide and no pass parts by more than 0.3%.

Recent work asks whether generative-engine visibility can be approximated with deterministic, engine-free page scores. We separate two stages such scores can conflate: exposure to a live engine and citation selection conditional on exposure. In an observational audit of ChatGPT, Microsoft Copilot, Google, and Perplexity, 15 fixed commercial prompts produced 589 citation observations on 6 June 2026, corresponding to 528 unique URLs and 356 domains. Same-prompt cross-engine URL overlap was extremely small: mean pairwise Jaccard similarity was 0.0079, the median was zero, and 84.9% of engine pairs shared no cited URL. On the ten prompts observed on all four engines, mean exact-URL Jaccard was 0.0072. A matched-size hypergeometric baseline preserving each prompt's four-engine URL universe and each engine's list length predicts 0.1272, so observed overlap was only 5.7% of that baseline; zero URL overlap occurred in 86.7% of comparisons versus 12.3% expected. Top-five exact-URL overlap was zero in all 60 pairwise comparisons. A single engine captured only 11.4%-42.6% of the four-engine URL union, and 96.4% of observed URLs appeared in only one engine. A separate 5-to-6 June same-engine comparison found 67.0% mean URL-set turnover. These results do not invalidate engine-free page scoring; they identify its estimand. A score computed without a live engine can estimate page quality or query-page fit, while end-to-end visibility additionally depends on engine-specific exposure and selection. We therefore argue for reporting page fit, observed exposure, conditional selection, and final visibility as distinct quantities.

Scientific knowledge in medical image analysis is shaped by venues such as the Medical Image Computing and Computer-Assisted Intervention (MICCAI) conference, which influence research agendas, professional credibility, and access to opportunity. As AI methods increasingly depend on large-scale data and compute, these dynamics risk further concentrating influence within already well-resourced regions and institutions. Prior meta-research on MICCAI has examined reproducibility, evaluation, and citation practices, but offers limited insight into who participates in and shapes the field. To better understand these dynamics, we conduct a longitudinal bibliometric analysis of the geographic and institutional structure of the MICCAI community, drawing on 9,748 papers published between 1998 and 2025. We find that the USA and China together account for nearly half of all publications, that high-income countries dominate collaboration networks as central and bridging nodes, while lower-income countries remain peripheral, and that participation inequality (Gini index 0.86-0.91 among contributing countries) has declined only marginally over 28 years. We further analyze the evolution of research topics between 2021 and 2025, distinguishing stable core pillars (e.g., segmentation, diagnosis, MRI/CT) from emerging paradigms (e.g., foundation models), and identify a persistent long tail of underexplored application-method and organ-modality intersections. To support transparency and reproducibility, we introduce the Atlas of MICCAI dataset and an interactive dashboard. We contextualize these findings within existing MICCAI equity initiatives, and propose actionable recommendations to reduce participation barriers, build research capacity, and recognize a wider range of scientific contributions.

Dilution of precision is the standard way to describe navigation geometry and it does not apply in cislunar space: its derivation presumes a snapshot solution in which simultaneous measurements determine the state at one instant. A spacecraft tracked by inter-satellite ranging in the Earth-Moon three-body problem has no such solution: range is a function of position only, so the velocity columns of the measurement Jacobian vanish identically and the state is unobservable however many links are in view. The correct figure of merit is dynamical, because the three-body flow carries velocity information into later range measurements. We demonstrate this on four differential-corrected planar distant retrograde orbits, reporting the observability Gramian rather than a dilution of precision. Instantaneous range-only geometry has rank 2 of 4; the full state becomes observable only after a tracking arc of 2.09 h, the first sampled arc at full rank on a 0.26 h grid, and a square-root information filter recomputing the same quantity by a different route becomes well-posed at exactly that arc. Beyond it, conditioning improves monotonically with arc length, the Gramian condition number falling from 1.2e11 at 3 h to 1.4e5 at 48 h. Adding range rate lifts the instantaneous rank from 2 to 4, so a Doppler-capable link makes a snapshot solution exist where a range-only link cannot. Lifting the known-reference assumption, the joint problem of estimating a station and the satellites' states and clocks together is rank-deficient by exactly one without an external interferometric observable in all twenty realizations tested, and full rank with it; the deficiency persists only to four satellites. For the configurations studied, cislunar navigation requirements are better written as arc-length, conditioning and measurement-type budgets than as dilution-of-precision thresholds, which are undefined here.

Total-body positron emission tomography (TB-PET) enables fast, low-dose, and dynamic imaging over a long axial field of view, but reconstruction remains challenging due to reduced counts, large image volumes, and increased data dimensionality. Generative models offer powerful learned priors for low-count PET, yet explicit PET measurement conditioning at TB scale has not been demonstrated. Inspired by PET decomposed diffusion sampling (PET-DDS), we propose TB-PET-DDS, a reconstruction framework that combines a CT-conditioned generative prior with patient-specific list-mode PET data. During reverse diffusion, PET consistency is enforced using a closed-form 3D TB-PET maximum-a-posteriori expectation maximisation fusion update, rather than relying solely on image-domain conditioning. The synthetic measurements are generated from the low-dose vendor reconstruction, providing a controlled inverse problem and retaining a full-dose reference. Proof-of-concept evaluation was performed on a single clinical TB-PET acquisition, with reconstruction hyperparameters selected against the full-dose reconstruction from the same case for all models. TB-PET-DDS improved NRMSE and SSIM relative to the DDIM and Image-DDS baselines, improving through-plane consistency in coronal views while enhancing agreement with the measured PET data. Although smoothed low-dose vendor reconstructions achieved the best global voxel-wise metrics, TB-PET-DDS produced the lowest liver coefficient of variation. These results demonstrate the feasibility of measurement conditioned diffusion reconstruction at TB scale and provide an initial route towards learned, projector-consistent generative reconstruction for low-count TB-PET imaging.

Physics-Informed Neural Networks (PINNs) provide a mesh-free framework for solving partial differential equations but often struggle with sharp gradients and shock-dominated solutions. Extended Physics-Informed Neural Networks (XPINNs) address this challenge through domain decomposition; however, the effects of decomposition design, overlap, and local network capacity on solution accuracy remain insufficiently characterized. This work presents a systematic assessment of domain decomposition configurations for XPINNs applied to the one-dimensional viscous Burgers equation ($\nu=0.01/\pi$). We compare a standard PINN, a conventional XPINN, a shock-focused XPINN with increased network capacity in the shock-containing subdomain, and overlapping XPINNs with different overlap widths. All configurations are trained using a common protocol based on Adam, L-BFGS refinement, and ten Residual-based Adaptive Refinement (RAR) cycles. Performance is evaluated against a reference solution using global and shock-region relative $L_2$ and $L_\infty$ errors, maximum PDE residuals, and interface continuity errors. The results show that decomposition design strongly affects XPINN accuracy and shock resolution. Among the overlapping configurations, the smallest overlap provides the best accuracy, while larger overlaps degrade performance. The shock-focused XPINN achieves the lowest overall solution errors, indicating that increased local network capacity can provide greater benefit than increasing overlap alone. RAR produces the largest improvements during early refinement stages, followed by increasingly non-monotonic changes in accuracy. These findings highlight the importance of jointly considering decomposition, interface coupling, network capacity, and adaptive refinement for shock-dominated problems.

Quantum Reservoir Computing (QRC) uses fixed quantum dynamics as a high-dimensional feature map. Still, standard pipelines flatten reservoir measurements and train a linear readout, ignoring the natural tensor structure across time steps, qubits, and observables. We propose a multilinear readout for quantum reservoir computing (ML-QRC), a tensor-structured neural readout compressed through mode-wise projections. Relative to a dense hidden-width-64 neural readout, this reduces the feature-to-hidden parameter count from $64TnF$ to $d(T+n+F)+64d^3$, giving a $12.1\times$ feature-block compression at $T=50$, $n=6$, $d=8$, and $F=n+\binom{n}{2}$. Across Mackey-Glass forecasting and TFIM phase classification, ML-QRC remains statistically competitive with Ridge on Mackey-Glass and obtains the numerically highest full-data TFIM accuracy among tested methods, while using $12.0\times$ fewer parameters than the full dense MLP. Its clearest benefit is improved low-data stability relative to neural MLP readouts on Mackey-Glass; this advantage does not transfer to TFIM, where Ridge performs best at 50% data. Overall, ML-QRC is best viewed as a tensor-structured neural readout that compresses dense MLP readouts while preserving QRC tensor structure, rather than as a replacement for simple linear/Ridge readouts in the tested regime.

Machine learning classifiers for bearing fault detection produce scalar confidence scores that conflate confident errors with genuinely ambiguous predictions, and the conventional truth/falsity pair (F = 1 - T) is algebraically redundant by construction. We operationalize a refined neutrosophic decomposition of a Random Forest + XGBoost + Logistic Regression ensemble into four indicators – T-hat (top-class evidence), F-hat (best-competitor evidence), predictive entropy I1-hat, and decision disagreement I2-hat – evaluated on two bearing benchmarks (CWRU and JNU, 600-1000 rpm) under a leave-one-condition-out protocol. On CWRU, after correcting a file-to-class mapping error, the ensemble reaches 100.00 percent accuracy on three of four held-out loads (92.27 percent on the fourth), leaving too few errors for uncertainty analysis. On JNU, holding out 1000 rpm, accuracy collapses to 40.64 percent, below a majority-class baseline; Logistic Regression (57.91 percent) generalizes far better than the tree ensembles. I1-hat shows a robust association with error beyond T-hat/F-hat, while I2-hat contributes little; standalone Logistic Regression confidence outperforms the full decomposition, a boundary condition we report honestly. Two further results extend this: fusing a time-domain and a frequency-domain model of the same signal and scoring their Jensen-Shannon divergence beats that model own entropy (AURC 0.29 vs. 0.36 on the standard split; 0.54 vs. 0.73 under a harder single-condition reproduction), the only indicator moving correctly under a CWRU-versus-JNU distributional-shift contrast; and, on CWRU alone, literature-verified bearing fault frequencies, correctly demodulated via the envelope spectrum, separate most fault classes almost perfectly (99.57 percent) using three interpretable features. Code, logs, and figures are released for independent verification.

We propose a computationally inexpensive algorithm to determine whether an opaque spherical body eclipses a luminous one, using only classical geometrical tools. We apply this method to the Sun-Earth-Moon system and predict solar eclipses, including their type, beginning, and duration, using the three-body problem. For predictions over a one-year period, the resulting errors are in the order of minutes.

Rapid and reliable identification of pharmaceutical residues is important for safeguarding public health, ensuring food safety, and enabling practical Raman-based screening. In this study, we propose HyMLRaman, a hybrid Raman spectroscopy framework that combines deep spectral feature extraction, generative models, and classical machine-learning classifiers to identify six pharmaceutical compounds, including amoxicillin, chloramphenicol, ciprofloxacin, tetracycline, ibuprofen, and paracetamol. Raman spectra are converted into spectral images and encoded with several deep neural-network backbones, among which EfficientNet-B3 yields the most effective representation. The resulting 1536-dimensional embeddings are then used to train downstream classifiers, including SVM, KNN, logistic regression, random forest, XGBoost, and ANN, using stratified 10-fold cross-validation. The hybrid EfficientNet-B3–SVM configuration achieves the strongest baseline performance, reaching 96.31% accuracy and a macro-F1 score of 96.36%, outperforming the standalone CNN baseline. To address limited-data conditions, a generative model, a DDPM-based feature augmentation, is introduced in a PCA-reduced EfficientNet-B3 latent space. The low-data ablation results show that DDPM augmentation provides selective benefits, particularly for KNN with reduced training fractions, and that its effect remains classifier-dependent. Finally, an application-level Raman Pharmaceutical Analyzer demonstrates the feasibility of embedding the trained model into an interactive Raman analysis workflow. These results suggest that HyMLRaman provides a practical and interpretable route for rapid Raman-based pharmaceutical screening.

Recent advances in motion generation and whole-body tracking have enabled humanoid robots to execute increasingly diverse motions, yet the same motion capabilities may be requested repeatedly during continual deployment. Reliable reuse is challenging because intervening motions can change the robot's entry state, making previously successful motions unsafe to replay blindly. Meanwhile, validated capabilities accumulate during deployment, while bounded storage requires deciding which ones are worth retaining. To address these challenges, we present HumanoidTTT, a framework for test-time capability reuse in continual humanoid control. Specifically, we introduce Selective Full-Motion Reuse, which authorizes direct reuse of validated complete motions only from certified applicable entry states, allowing accepted reuse to bypass fresh generation. We further introduce Test-Time Capability Consolidation, which adapts which qualified capabilities persist in a bounded Full-Motion Store using subsequent deployment reuse as feedback. Experiments demonstrate zero unsafe accepts and a 16.4$\times$ end-to-end speedup over fresh generation, while online consolidation improves avoided generator calls by 13.2 per 200 requests over its frozen counterpart. Overall, HumanoidTTT enables reliable and efficient reuse of validated motion capabilities while adaptively retaining useful capabilities throughout continual deployment. Code: https://github.com/AIGeeksGroup/HumanoidTTT. Website: https://aigeeksgroup.github.io/HumanoidTTT.

We investigate automated rewards for training language models in conversational humor, focusing on reward exploits and countermeasures. Two approaches aim to capture understandable surprise and predicted audience amusement. Controlled tests show that an embedding-based surprise reward accepts word-shuffled replies as readily as witty ones. A fluency filter detects the shuffles, but the combined reward also rejects some witty replies and fails further validation. An audience model's predicted laughter is instead vulnerable to laughter cues in either speaker's messages. Normalizing these cues across speakers blocks the covered attacks, although unmatched expressions remain exploitable. Three reinforcement-learning runs evaluate training with successive reward revisions. The final run improves the combined evaluation score by 0.0903 and reduces zero-score sessions by 40%, but its humor-specific improvement remains below our preregistered target. These findings illustrate a broader challenge for automated reward design: countermeasures must block exploitable shortcuts while preserving the behavior the reward was intended to encourage.

Multimodal large language models (MLLMs) have shown strong potential for video understanding and caption generation, but their performance may decline in specialized medical imaging domains such as echocardiography. This work introduces Gaussian Process Embedding Correction (GPEC), a modular and computationally efficient pre-LLM error-correction method that improves the visual representations used by VideoChat2 for cardiac ultrasound caption generation. GPEC is inserted between the visual projection layer and the language model and learns a residual correction that moves the projected visual representation toward an annotation-guided target. The target is constructed by converting structured video annotations into qualitative attributes, generating a fixed-format reference caption, and mapping it into the language-model embedding space. The correction is modeled using a sparse variational Gaussian Process with inducing points, natural-parameter variational updates, and a block-wise linear kernel, while the original VideoChat2 components remain frozen.The method is evaluated using representation-level, caption-level, content-oriented, and execution-time metrics by comparing the original VideoChat2 with VideoChat2 + GPEC under identical input and reference conditions. Results show improved caption similarity and content alignment after applying the proposed correction. Furthermore, GPEC adds less than 0.05 s of inference-time overhead per video in the evaluated setting. These findings indicate that GPEC can improve caption generation in specialized medical video domains with minimal computational cost, without requiring end-to-end fine-tuning of the pretrained multimodal backbone.

Recent advances in Gaussian Splatting (GS) compression have enabled substantial reductions in GS model size. Reliable objective quality assessment is therefore essential for comparing compression methods and guiding the development of more efficient GS codecs. Existing GS quality assessment typically relies on image and video quality metrics, requiring rendering of predefined viewpoints and making the quality estimate dependent on the selected views. This paper introduces GS-PQM, a novel full-reference quality metric for post-training GS compression that operates directly in the GS parameter domain. GS-PQM estimates perceptual quality from a set of parameter-domain distortion errors using a Support Vector Regression model. Experimental results show that GS-PQM outperforms 25 existing image, video, and point-cloud quality metrics in assessing compressed GS content, providing an accurate and computationally efficient alternative to rendering-based quality assessment.

Holographic dark energy ties the dark-energy density to an infrared length. We study new Tsallis holographic dark energy (NTHDE), built on the exponential Tsallis entropy, with the local Granda-Oliveros (GO) cutoff $L^{-2}=\alpha H^2+\gamma\dot H$ in a spatially curved universe. Writing the background as an autonomous system for $(\Omega_d,u,\Omega_k)$, we obtain four exact results. (i) In the closed-form solution without the Tsallis deformation, the dark energy splits into a matter-like and a curvature-like part. (ii) Because the GO cutoff lacks the term $k/a^2$ of the Ricci scalar, the coefficient of $(1+z)^2$ in $H^2/H_0^2$ is $R_k\Omega_{k0}$ with $R_k=(1-\alpha+\gamma)^{-1}>1$, while distances and the Clarkson-Bassett-Lu test return $\Omega_{k0}$; the Ricci completion restores $R_k=1$. (iii) Big-bang nucleosynthesis locks the matter-era dark-energy fraction to $1/(1+3|w_{\rm GO}|)$, where $w_{\rm GO}$ is the equation of state of the GO mode. (iv) The finite-time fold singularity of the flat model survives curvature. Against Pantheon+SH0ES supernovae, 32 cosmic chronometers and DESI DR2 BAO, curved GO-NTHDE gives $\Omega_{k0}=-0.001^{+0.041}_{-0.043}$, consistent with flatness, and $\Delta\chi^2=-2.82$ relative to flat $\Lambda$CDM, but the Bayesian evidence prefers flat $\Lambda$CDM ($\ln B=-2.66\pm0.24$), and allowing curvature costs $\ln B=-1.39\pm0.25$. The data cannot yet measure $R_k$: the GO and Ricci cutoffs fit equally well ($\ln B=+0.28\pm0.26$). With Union3 supernovae the model is on a par with $\Lambda$CDM ($\ln B=+0.53$). A fraction 0.91 of the posterior reaches the finite-time fold.

For a positive integer $m$ and a real parameter $\alpha>-1$, consider the generalized Cesàro matrix on $\ell^2(\mathbb N_0)$ with entries $m(n-j+1)_{m-1}/(n+\alpha+1)_m$ for $j\le n$. We give a computer-assisted proof that this operator is hyponormal if and only if $\alpha\ge0$. The main algebraic ingredient is an explicit decomposition of an auxiliary defect operator into a positive diagonal operator and at most $m$ rank-one operators. Discrete Gram polynomials determine the signs and coefficients of these terms. For nonnegative parameters, weighted estimates reduce positivity to scalar inequalities. A uniform analytic estimate covers every $m\ge32768$, while finite rational certificates cover the remaining orders and entire parameter intervals, without parameter sampling or truncating an infinite operator. The proof also gives a uniform weighted lower bound for the self-commutator. For $-1<\alpha<0$, finite-support vectors give negative quadratic forms for every order.

We show how migration between counties in different cities can explain both the population scaling of mean intercity flows and heavy-tailed intercity net-flow distributions. Density-dependent departure and arrival activities determine how mean flows scale with the populations of the origin and destination cities. We assume Gaussian county-pair net flows with standard deviations proportional to their mean directional flows. At a fixed correlation between county-pair net flows, their sum is Gaussian. Averaging this conditional Gaussian density over the correlation distribution can produce an intermediate power law with a Gaussian cutoff. We also present a stochastic model that generates the variance distribution used in this mixture.

Modeling protein-protein interactions requires accurate scoring functions that can rank potential poses (conformations) of a protein-protein complex to differentiate near-native poses from incorrect ones. Here, we propose a general framework for improving protein-protein pose ranking and other biomolecular interaction models using the LambdaLoss loss function from the Learning-to-Rank field. We test this framework by fine-tuning the energy prediction head of DFMDock with the LambdaLoss on an augmented dataset of 2.9M decoy poses derived from the DIPS dataset. On targets from the CAPRI score set benchmark, our fine-tuned ranking model LambdaDockScore is better at identifying correct poses in its top-1 and top-5 predictions compared to EuDockScore, a state-of-the-art method. LambdaDockScore also improves upon baseline DFMDock ranking performance for scoring antibody-antigen complexes and protein-protein complexes with very large or small binding interfaces.

We study online convex optimization on a bounded Euclidean domain when the learner receives only one subgradient at its prediction and knows neither the horizon, a gradient bound, nor the losses' strong-convexity parameters. We present a scale-invariant algorithm that couples projected adaptive gradient descent to one cone-constrained quadratic leader through a positive wealth process. The algorithm maintains $O(d)$ state, without a learning-rate grid or restarts. For a domain of diameter at most $D$, it guarantees regret at most $\sqrt{2}D(\sum_t\|\widehat g_t\|^2)^{1/2}+2D\max_t\|\widehat g_t\|$, with no logarithmic factor. A simultaneous quadratic-distance bound yields explicit improvements for unknown strong convexity, including a refinement governed by jumps in the observed gradient scale. For varying per-round curvature, the bound depends on the total shortfall below a reference level selected in hindsight. The proof uses a clipping-compatible surrogate and a potential involving the quadratic minimum, log wealth, and two scalar curvature statistics. The resulting strongly convex bound is not uniform at the classical logarithmic rate over all curvature-to-gradient ratios; the exact parameter dependence is stated. The contribution is a single-leader construction and its analysis, within an established literature on universal and scale-free online learning.

Diffusion maps, and kernel methods more generally, provide an interpretable nonlinear spectral representation basis for geometric learning. In the geometric limit, small bandwidth, these matrices tend to be high rank and thus require materializing dense Gaussian kernels requires $O(N^2)$ memory. We introduce FlashDiffusion, a matrix-free method that evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical $\beta$-flow that selects the finite-sample resolution scale. A continuation over sample size and bandwidth warm-starts increasingly expensive spectral solves from coarser resolutions.

Financial time-series forecasting must capture price dynamics across heterogeneous assets while incorporating news available at prediction time. We introduce DualCast, a dual-path framework that extends a frozen language model with a discrete financial vocabulary. Each log-return patch is represented by a learned summary token and three residual shape tokens, preserving local drift and volatility while allowing shape patterns to be shared across assets. To improve codebook utilization, we develop adaptive frequency-equalizing residual vector quantization, which rebalances overloaded codewords without compromising reconstruction accuracy. The fast path trains only the new financial-token embeddings and output heads on a frozen Qwen3-8B backbone. A toggleable LoRA adapter enables a slow path that conditions on the fast forecast and news available at the forecast origin to produce a revised prediction. The reviser is initialized by supervised fine-tuning and further optimized with a return-space group relative policy optimization objective that rewards improvements over the fast forecast. In zero-shot evaluations covering equities and energy prices at five-minute, daily, and weekly resolutions, the slow path achieves the lowest mean absolute percentage error among the compared methods in 8 of 12 dataset-horizon settings, including every longest-horizon setting. News ablations indicate additional gains in most tested settings, although their magnitude varies across markets. DualCast thus combines a fast numerical forecaster with an optional text-conditioned revision mechanism.