Papers

Medical image segmentation models typically rely on large amounts of densely annotated volumetric data, limiting their scalability across tasks and imaging modalities. This work addresses the challenge of predicting entire 3D anatomical structures from extreme annotation sparsity. An annotation-efficient student-teacher framework is proposed for automatic 3D medical segmentation that requires only a set of point prompts on a single 2D slice per volume, as input. A foundation model serves as an offline teacher, utilizing the provided point prompts from the selected slice to full-volume pseudo-annotations alongside their corresponding spatial confidence scores prior to student training. To mitigate the error propagation of noisy pseudo-annotations, a task-specific 3D student network is trained using a confidence-aware optimization strategy. By leveraging the teacher's pre-computed confidence scores, this strategy explicitly excludes statically uncertain regions of the pseudo-annotations from the loss calculation, while simultaneously emphasizing regions with higher confidence. Evaluated on 3D cardiac MRI datasets, our framework outperforms state-of-the-art semi-supervised methods, improving segmentation performance by up to 43.6%. Furthermore, it drastically reduces the manual annotation burden to just a few positive point prompts per volume, while improving surface boundary precision by up to 14.7% over the teacher and successfully recovering up to 34.1% of the performance gap toward the fully supervised upper bound.

The cancer specificity of serum prostate-specific antigen (PSA) motivates complementary, non-invasive approaches to prostate disease assessment. Building on reported high-resolution terahertz (THz) analysis of urine-derived products, this review integrates spectroscopic evidence with a statistical reanalysis of clinical data from 24 patients with prostate cancer (PC) and 14 with histologically confirmed benign prostatic hyperplasia (BPH). Nonparametric statistical comparison shows higher PSA levels in PC, while overlapping patient distributions and receiver-operating-characteristic analysis with bootstrap uncertainty estimation demonstrate incomplete discrimination from BPH. Fast frequency-sweep spectroscopy characterizes urine-derived volatile and thermal-decomposition products, distinguishing compounds shared between groups from candidate PC-associated assignments, including glycolaldehyde, butyronitrile, pentanenitrile and methyl isocyanate. Glycolaldehyde has been detected by urinary carbonyl profiling, while benzaldehyde and phenol have been reported in urinary volatile studies. Related aldehydes identified by gas chromatography-mass spectrometry and glycine-associated metabolites reported in proton nuclear magnetic resonance studies provide complementary chemical and metabolic context. These correspondences support plausibility of THz findings without establishing PC specificity. Together, the dataset, statistical assessment and comparative literature synthesis support THz urine spectroscopy as a platform for molecular discovery and candidate prioritization. Standardized sample preparation, separation of native urinary constituents from processing-derived products, and validation in independent cohorts remain necessary.

Classical electrodynamics including Lorentz-invariant classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the action variables analogous to those appearing in the Bohr theory of the hydrogen atom. Thus there is a purely classical electromagnetic derivation of the Bohr energy levels. According to classical electromagnetic theory, it is not that there are states where the charged particle does not radiate, but rather in these states there is a resonant balance between radiation emission and absorption The work on classical zero-point radiation reported here is a continuation of the analysis published in 1975, but with the addition of the ideas of relativity and resonance between the charged-particle orbit and classical zero-point radiation.

Dictionary learning seeks to recover an unknown dictionary $A$ from observations ${\bf y}_i = A{\bf x}_i$ with sparse coefficient vectors ${\bf x}_i$. We introduce the Iterative Atom Refinement (IAR) algorithm, a simple procedure for recovering individual dictionary atoms. Starting from a random direction, IAR repeatedly selects the observations most strongly correlated with the current iterate and updates the direction by averaging the selected data. Our main contribution is a rigorous convergence theory of IAR. Using high-dimensional probabilistic estimates and a novel monotonicity principle for atom-selection probabilities, we show that a small initial advantage of one atom is amplified until that atom is isolated. Under our model assumptions, IAR identifies a generating atom after only three refinement steps. Numerical experiments support the theory and show that the resulting dynamics accurately capture the behavior observed in dictionary refinement.

Whether a full counting statistical distribution preserves its universality class across a coherent-to-incoherent crossover is a fundamental question in open quantum systems. We resolve this for the infinite-$U$ Hubbard chain, showing that local density dephasing changes transport exponents without destroying the underlying non-Gaussian M-Wright spin fluctuations. Utilizing the exact spin-charge composition law inherent to impenetrable dynamics, we track the charge sector from ballistic flow to diffusive hydrodynamics. This dissipative crossover shifts the characteristic spin-transfer width from $t^{1/4}$ to $t^{1/8}$. Despite this altered scaling time, the central spin characteristic functions uniformly collapse onto a singular M-Wright scaling function, what we confirm using analytics as well as numerics.

Low-rank approximation is a fundamental tool for scalable matrix computations. While such approximations have classically been formed via the truncated SVD, recent advances in randomized numerical linear algebra have produced methods of comparable accuracy at a fraction of the cost. A key advantage of these approaches is their ability to operate with limited access to the full matrix. A prominent example is the CUR decomposition, which builds an approximation from only a subset of columns and rows, making it particularly well-suited to settings where global matrix access is unavailable, such as in the design of spectro-microscopy experiments where even matrix-vector products cannot be computed. However, the randomness inherent to these methods introduces a key challenge: efficiently assessing approximation accuracy under the stringent constraint that only a subset of matrix entries can be observed. We derive a "blind" estimator of the Frobenius error of a CUR decomposition. For this estimator, we derive a worst-case lower bound on the number of required column queries, and provide techniques for quantifying its uncertainty. Finally, we demonstrate the performance of the estimator and the uncertainty sets on a mix of synthetic problems and real spectro-microscopy examples.

Coding agents are extended by plugins: installable bundles that ship skills, sub-agents, commands, hooks, and tool servers. On 24 July 2026, an open specification (Agent Plugins v1.0.0) standardised how such a bundle is laid out and described, so that one plugin could run on any agent. We ask the two questions a practitioner would ask of it: is the ecosystem adopting the standard, and if a plugin did conform, would that be enough to make it work alongside the other plugins a user has installed? We answer both by building AgentPluginZoo, a provenance-tracked corpus of 68,072 plugin bundles across 30,655 repositories, released with its discovery ledger, scoring code, and analysis. Only 6.2% validate, but the gap is shallow rather than structural: 96.6% would load after adding one missing boilerplate field. The real cost lands elsewhere. 40.2% would load while the specification obliges the client to discard fields their authors wrote, mostly declarations of what the plugin ships. Moreover, conformance settles nothing for the second question: 81% of capability-exporting bundles share a name with another plugin, with no namespace or precedence rule to decide which one answers. This paper argues the community standardised a packaging format when composition needs a model, names the four concepts such a model must add - qualified capability identity, a declared capability surface, a precedence rule, and inter-plugin relations - and shows they fit an additive v1.1 profile of the same specification rather than a competing standard. Recommendations follow for practitioners packaging extensions today and for the people evolving the standard, chief among them that conformance must be made observable before it can become common. The corpus and code are available at https://github.com/tezansahu/agentpluginzoo

While test-time scaling enhances Large Language Model (LLM) agents in long-horizon software engineering (SWE), sparse binary rewards (Pass/Fail) create a severe credit assignment crisis and waste failed exploratory trajectories. Current trajectory optimization and scaling methods are costly and structurally limited, relying on heuristic state reuse without causal diagnosis or delayed scalar scoring without actionable online guidance. We propose FLARE (Full-Lifecycle Alignment and Reward Engine), a novel dense supervision paradigm driven by a lightweight Generative Reward Model (GRM). First, RADAR, an offline causal-aware diagnostic framework, extracts high-fidelity, hindsight-free supervision through causal-chain backtracking to distill a GRM providing real-time, step-level risk feedback. Second, FLARE uses this GRM to continuously optimize the agent across its entire lifecycle. During inference, FLARE acts as an Active Scaffold, autonomously intercepting high-risk generation steps for localized breakpoint re-execution, drastically reducing compute overhead. During post-training, the GRM's structured signals serve as process-supervised reranking scores for Supervised Fine-Tuning (SFT) and step-level dense rewards for Reinforcement Learning (RL), mitigating policy collapse in sparse environments. Extensive evaluations show that FLARE establishes a new Pareto frontier across the agent lifecycle: FLARE (N=1) outperforms Global Rollout (N=5) with a 5x reduction in token consumption. Extending FLARE to training overcomes the sparse reward problem in long-horizon interactive tasks, delivering relative performance gains of 19.13% in SFT through process-aware data curation and a consistent 9.19% improvement in RL.

Leading commercial and open-source Text-to-Speech (TTS) models fail to emulate the regional phonetic diversity of Brazilian Portuguese (pt-BR). By aggregating disparate dialects into a single training distribution, they generate a synthetic "diluted" accent: a phonetic profile attempting to represent all regional distributions simultaneously, but ultimately carrying phonological ambiguity dissociated from natural socio-phonetic realizations. This work introduces a speech deepfake detection methodology combining multilingual phone recognizers with classical signal processing to extract phoneme-level features in consonantal and vocalic realizations with high geographic variance. The analysis reveals that the distributional gap over these features suffices to distinguish natural and synthetic voices through unsupervised Kernel Density Estimation, establishing dialectal inconsistency as a useful and interpretable feature for spoofing detection in pt-BR. Evaluation on pt-BR anti-spoofing datasets shows that these explainable, lightweight, low-dimensional features can boost the performance of foundation models on the task, and show generalization capabilities in a cross-dataset leave-one-out setup.

Many knowledge-work benchmarks are constructed around individual tasks, with the context needed for each task selected together with or after the task has been specified. This design measures performance on workplace-like tasks in an environment assembled for the task. When task specification guides which context is selected, the evaluation can encode task information into the environment and pre-complete part of the information-localization work that workplace performance normally requires. We introduce WorkWorlds, an evaluation infrastructure that separates organizational state from task specification. A world first fixes a revision, date, and employee seat and materializes the organizational state that employee can access; tasks are introduced only afterward. We implement WorkWorlds in a primary synthetic pharmaceutical company with 8 measured tasks across 6 employee seats, and construct additional organizational worlds. Across 192 matched evaluations, task-level curation increased evidence access by 17.6 percentage points, from 72.8% to 90.4%, and criterion pass by 8.7 points, from 68.0% to 76.7%, while pass conditional on evidence access remained nearly unchanged; most of the measured difference occurred before the agent reached sufficient evidence.

Identifying the poorest communities is essential for poverty alleviation, but household surveys and censuses are costly and infrequent. Machine learning offers alternative poverty estimates from mobile phone and satellite data, yet average prediction accuracy alone does not show whether maps support targeting under limited budgets. We apply a decision-centered evaluation to 13,985 Grama Niladhari divisions in Sri Lanka, combining call detail records (CDRs), remote sensing (RS), and CNN-derived Landsat 8 embeddings. We assess recovery of the poorest administrative units, compare random and spatially grouped validation, and examine errors in socioeconomically atypical communities. Against a census-derived asset index (PC1), Random Forest achieves Recall@25% of 0.830, compared with 0.450 for nighttime lights. Random splitting raises recall by 4.1 percentage points relative to Divisional Secretariat Division (DSD)-grouped holdouts. The combined model recovers 86% of the 25 poorest DSDs by PC1, versus 69% for RS-only and 67% for CDR-only models. Spatially isolated divisions have 10.8% higher prediction error. Stronger isolation–error association in RS-only models is consistent with spatial smoothing, although its cause remains unconfirmed. These findings support evaluating poverty maps by targeting performance and geographic transfer, while recognising that agreement with an asset index does not establish consumption-poverty accuracy.

We characterize the essential spectra of normal operators admitting normalized orbit frames. These are exactly closed subsets of the unit circle with positive Haar measure.

A majority coloring of a graph $G$ is a vertex coloring of $G$ in which no vertex has more than half of its neighbors colored with its own color. The least number of colors required for a majority coloring of $G$ is the majority chromatic number $\mu(G)$. The majority coloring game, introduced by Bosek et al. (2019), is a two-player Maker-Breaker-type game where the players alternately color vertices while maintaining the majority condition at each vertex; the least number of colors required for the first player to have a winning strategy on $G$ is the majority game chromatic number $\mu_g(G)$. In contrast with the static case, Bosek et al. show that $\mu_g(G)$ is unbounded in general, while $\mu_g(G)\le col_g(G)$, where $col_g(G)$ is the game coloring number of $G$. It is known (cf. Faigle et al. (1993)) that, for any acyclic graph $G$, $col_g(G) \leq 4$, so $\mu_g(G) \leq 4$ as well. We improve this bound by showing that $\mu_g(G) \leq 3$ for any acyclic graph $G$ of maximum degree at most $4$. We also show that $\mu_g(G) = 2$ if $G$ is a nonempty path, star, or complete graph, or a disjoint union of such graphs. These improve the results of Bosek et al. We also initiate the study of the computational complexity of the pre-coloring extension problem for the static and game versions of majority coloring. We show that the Majority $k$-precoloring Extension problem is NP-complete for each $k \geq 2$. When $k = 2$, it remains NP-complete on the class of bipartite graphs where maximum degrees of each part are $5$ and $6$, and when $k = 3$ it remains NP-complete on the class of $12$-regular planar graphs. We show that the game version is PSPACE-complete, even when the number of colors $k=\chi(G)$, and even when $k=2$ and $G$ is a bipartite graph in which one part has maximum degree equal to $9$. The results on the game versions also hold for the variation where Bob starts the game.

We study the graph distance $D_n(p)$ and effective resistance $R_n(p)$ between the boundary vertices of a depth-$n$ random series–parallel graph, obtained by recursively joining two independent copies in series with probability $p$ and in parallel with probability $1-p$. We prove the existence of deterministic logarithmic speeds: for every $p\in[0,1]$, $n^{-1}\log D_n(p)$ and $n^{-1}\log R_n(p)$ converge to deterministic limits $v_D(p)$ and $v_R(p)$, respectively, almost surely and in $L^1$. The limiting speeds agree with the corresponding first-moment logarithmic rates for every $p\in[0,1]$ in the distance case and for $p\in[1/2,1]$ in the resistance case. We further determine the near-critical behavior of the resistance speed: $v_R(\frac12+\delta)\sim 2\zeta(3)^{1/3}\lambda_*\delta^{2/3}$ as $\delta\downarrow0$, where $\lambda_*>0$ is characterized by an explicit nonlinear boundary-value problem. This exponent $2/3$ contrasts with the exponent $1/2$ for distance obtained by Chen, Derrida, Duquesne, and Shi (2026). The main idea of this work was proposed by ChatGPT 5.6 Sol, and the authors take full responsibility for the mathematical content. The three main theorems and their supporting proof dependencies have been formalized in Lean 4, relative to two explicitly documented external mathematical inputs.

ABRIDGED We investigate the temporal evolution of the intrinsic polarization of the 2011 eruption of the recurrent nova T Pyxidis and use its continuum and line-polarization signatures to constrain the geometry and kinematic structure of the ejecta. We analyzed nine epochs of VLT/FORS2 optical linear spectropolarimetry obtained between 24 and 70 days after discovery, from shortly before optical maximum to the early decline. The instrumental and interstellar polarization contributions were removed, with the latter estimated from the depolarization observed at the rest wavelengths of the Balmer emission components. We examined the continuum and the velocity-dependent intrinsic polarization across the Hbeta, Hgamma, and Hdelta P Cygni profiles. The intrinsic continuum polarization generally remains below 1% and is predominantly aligned at a position angle of approximately 95degrees, except near optical maximum, when an orthogonal component at approximately 185degrees temporarily dominates. The blueshifted Balmer absorptions display stronger polarization, frequently reaching 2%, associated with excursions and loops in the Q-U plane. At least two distinct velocity-dependent polarization components are detected: the higher-velocity absorption is preferentially associated with the 95degrees orientation, whereas the lower-velocity absorption generally traces the 185degrees orientation. The polarization peaks shift quasi-linearly towards higher blueshifted velocities with time in all three Balmer lines.

High-precision connector insertion remains challenging for robotic systems due to tight mechanical tolerances, partial observability during contact, and multimodal uncertainty arising from occlusion and contact ambiguity. Successful insertion requires closed-loop contact guidance that continuously integrates global alignment cues with local contact feedback to produce stable corrective actions under interaction. In this work, we present ContactDP (Contact-Guided Diffusion Policy for Tight Insertion Tasks), a multimodal diffusion-policy framework for contact-rich insertion. ContactDP jointly integrates wrist RGB observations, fingertip tactile sensing, and wrist-mounted force-torque measurements to infer contact state and generate temporally consistent corrective motions during insertion. To ensure stable execution under contact, the learned policy operates together with a hybrid position-force controller that provides compliant low-level interaction. We evaluate our approach on a suite of industrial-grade connector insertion tasks with varying connector geometries, grasp conditions, and initial misalignment. Across all tasks, ContactDP significantly outperforms vision-only diffusion policies for performance, reliability and generalization.

A signed pairwise graphlet encoding of the velocity gradient tensor $\bm{A}$ is introduced as a minimal discrete representation of its off-diagonal structure, and its statistical relationship with the PQR topology of homogeneous isotropic turbulence is investigated using direct numerical simulation data at $Re_\lambda \approx 433$. Each off-diagonal component is assigned a ternary label based on a local threshold, mapping the thresholded off-diagonal sign pattern to one of $3^6=729$ discrete states. The imbalance $\Delta n=n_W-n_S$ between rotation-promoting and strain-promoting pairs is shown to act as a robust proxy for the sign of $Q$: $P(Q>0\mid\Delta n)$ increases monotonically from $0\%$ at $\Delta n\leq-2$ to $100\%$ at $\Delta n=+3$, and graphlets with a single rotation-promoting pair $(\Delta n=+1)$ predict the stable-focus-stretching region with probability approximately $65\%$ -nearly double the global base rate of $36.5\%$- despite discarding all magnitude information. This predictive power can be largely attributed to the off-diagonal contribution of $\bm{A}$, which dominates the sign of $Q$ in a majority of flow states. The graphlet–PQR association remains statistically correlated over several Kolmogorov time scales and exhibits spatial coherence comparable to that of the $Q$ field at dissipative scales, providing a consistency check that the discrete thresholding preserves the short-range organisation inherited from the velocity-gradient field. An out-of-sample predictive log-loss test further shows that $\Delta n$ captures most, but not all, of the predictive content of the complete $729$-state graphlet code: the full code retains a small, reproducible gain of order $10^{-3}$ bits per observation in predicting future PQR topology beyond $\Delta n$ and the continuous invariants, present at finite lag and absent at zero lag.

Early-phase combination oncology trials increasingly seek the optimal biological dose combination (OBDC) rather than a maximum tolerated dose combination, in line with the FDA's Project Optimus initiative. Existing Bayesian OBDC designs span rule-based, model-assisted, and model-based paradigms, but no unified framework exists for choosing among them, and none supports borrowing information across indications sharing a combination regimen. We propose a corrected three-by-two taxonomy of OBDC designs by mechanism and objective, a rule-based design (Ji3+3-Comb) closing a documented gap in transparent, model-free combination dose-finding, and a Bayesian Hierarchical Utility-based Cross-indication (BHUC) design that borrows information across indications via a robust mixture prior while discounting non-exchangeable information. We derive the shared utility function as the Bayes-optimal decision under a linear clinical loss, and prove that BHUC's mixture-prior posterior weight automatically vanishes as two indications' true rates become discordant, formalizing its robustness to non-exchangeable borrowing, and complement this asymptotic guarantee with an exact, sample-size-free ceiling on borrowed influence that holds even before any own-indication data accrue. A roadmap links trial features to design choice, and a 5000-replication simulation study, sensitivity analyses, and a case study built from a published phase Ib trial show that model-assisted designs offer the most robust safety-efficacy trade-off, while BHUC improves correct selection over independent per-indication designs even under discordance. We conclude with concrete, protocol-actionable recommendations for pharmaceutical and trial biostatisticians, and directions for future methodological and computational development.

Human motion is shaped by both external acoustic events and behavioral intent: spatial audio conveys environmental cues that elicit or guide a response, while text specifies the desired action and how it should be performed. In this paper, we study the novel task of human motion synthesis jointly conditioned on spatial audio and natural language, a problem that has been largely overlooked in previous research. To support this task, We introduce STAM, a dataset of motion sequences paired with spatial audio and detailed textual annotations whose rich vocabulary affords precise and nuanced specification of human motions. We further introduce MoSAT, a latent flow-matching framework for full-body motion generation jointly conditioned on natural-language intent and directional spatial-audio cues through hierarchical cross-attention before generating motion. Such a hierarchical design enhances temporally coherent and semantically aligned motion sequences. We also develop tri-modal evaluators for comprehensive evaluation on this novel task. Extensive experiments show that MoSAT achieves the SOTA performance by leveraging spatial audio's intrinsic motion-shaping properties alongside textual semantics, enabling precise and diverse motion in various scenarios.

Single-image 3D object generation can now produce high-fidelity assets, yet accurately placing them into a coherent scene layout remains an open challenge. A central difficulty lies in how object layout is represented. Holistic methods absorb placement into a scene-level generation process, sacrificing object-level detail. Compositional methods preserve object fidelity by decoupling geometry from layout, but typically parameterize layout as sparse, unbounded pose variables that are difficult to learn and generalize poorly under scarce scene-level supervision. We present Mira-Scene, a compositional 3D scene reconstruction framework that replaces sparse pose regression with dense, bounded correspondence recovery. At its core is the Canonical Coordinate Map (CCM), a pixel-aligned field that maps each visible object pixel to a surface coordinate in the object's bounded canonical space. When paired with a scene-space Point Cloud Map (PCM) from monocular geometry estimation, CCM induces dense canonical-to-scene correspondences from which object transformations are recovered through robust geometric alignment. Because CCM operates in bounded canonical space, it provides a stable prediction target that can be trained from scalable object-level 3D data without requiring scene-level layout annotations. Mira-Scene further introduces a multimodal diffusion transformer that jointly generates object geometry and CCMs, using modality-specific expert streams with shared attention and positional encoding to promote geometry-layout consistency. Experiments on indoor, outdoor, synthetic, and in-the-wild scenes show that Mira-Scene substantially outperforms strong baselines in layout accuracy, achieving relative gains of 39.8% in 3D-IoU and 16.5% in 2D-IoU over SAM3D, using limited open-source training data.

We investigate the equilibrium thermodynamics of a Dyson gas in connection with a set of integrable statistical mechanical observables satisfying the Toda Lattice hierarchy. We prove that in the thermodynamic limit, the integrable observables are state functions satisfying a set algebraic equations of state in closed form, obtained from direct integration of the Toda Lattice hierarchy in the continuum limit. We then explore the connection between regularity and critical behaviour of the state functions and the Dyson gas particle statistics via Monte Carlo simulations. We show that the properties of the integrable observables, such as regularity, multivaluedness, cusp singularities, carry information on the macroscopic particle statistics and its qualitative changes but with some limitations.

We address the problem of determining the degeneracy of a particular energy eigenvalue corresponding to a quantum particle trapped in a cubic box. In other words, we aim to find the number of ways a specific positive integer can be written as the sum of three natural number squares. This is a classic problem in number theory. We provide a closed-form, exact solution to the problem. We do not claim to provide proofs, as we have none; instead, we build up the formulae starting from simple cases where the answer could be deduced by studying the list of degeneracies. We present ample examples that could be verified against the degeneracy calculated numerically via the brute-force method. We arrived at the solution by meticulously studying the list of degeneracies for the first five million numbers, generated by Mathematica$^{\circledR}$.

Purpose: Alpha particles from $^{214}$Po, $^{212}$Po, and $^{210}$Po are increasingly used to calibrate large liquid scintillator detectors, but Geant4 simulations of their energy deposition require detailed validation. Methods: We simulate alpha particles in a 4 m cube of LAB-based liquid scintillator with Geant4 11.4.2 and apply Birks quenching per step. We study step-size, production-threshold, Birks-constant, and electromagnetic-model dependence, and use Geant4-DNA to examine keV-scale electron track structure. Results: Delta-electron-associated fluctuations dominate the simulated response. Across the tested explicit-delta settings, the variance of the quenched-response contribution from secondary tracks is 1.01–1.12 times the total variance; a negative primary–secondary covariance reduces the total. The simulated quenching-curve shape is compatible with SNO+ data within current uncertainties, with $\chi^2/\mathrm{ndf}\simeq0.14$–$0.17$ for $k_B=0.007$–$0.010$ g cm$^{-2}$ MeV$^{-1}$. Geant4-DNA gives strong electron-track curvature, with tortuosity decreasing from about 6 at 200 eV to 1.6 at 10 keV. Conclusion: Delta-electron fluctuations are the dominant contribution to the intrinsic resolution in the tested configurations. The production threshold has a larger effect than the electromagnetic model: Penelope and Livermore agree within about 3% in L/E, whereas Standard gives higher L/E, especially at low thresholds.

We consider robotic motion planning and control under unknown dynamics with hybrid state observations, where state measurements are available only in parts of the state space. Existing work combines system identification, predicted reachability, graph search and controller synthesis in a hierarchical framework using local affine approximated models over polytopic state space partitioning, but requires state observations for identification and feedback control. Based on this framework, we address blind regions by selecting nominal dynamics and precomputing open-loop control sequences before observation is lost. Since the true dynamics may differ from the selected nominal model, the robot may exit a blind polytope through an unintended facet. We quantify this transition risk and incorporate the possible outcomes into a stochastic transition system. The high-level planning problem is formulated as a stochastic shortest path problem, whose policy guides controller synthesis. A case study demonstrates that the method guides the robot from an initial state to a target while balancing route efficiency and the risks associated with traversing blind regions.

Plasma transport produced by electrostatic fluctuations is studied using a test particle model in a toroidal geometry. A model wave spectrum is assumed which introduces a time dependence in the Hamiltonian description of particle motion in the strong magnetic field. This allows for the existence of chaotic particle motion which gives rise to transport processes. Another way of producing transport is by introducing a stochastic process inside the wave spectrum. The two possibilities are explored and it is shown that both cases give rise to diffusive transport. The presence of chaotic motion is corroborated by computing approximate Lyapunov exponents. Additionally the presence of zonal flow is considered which can give rise to a transport barrier by suppressing radial particle fluxes, in the cases that show chaotic transport. This effect gives support to the existence of chaotic motion as responsible for transport since it reproduces the behavior of the robust invariant torus resilience to chaos, acting as a transport barrier, observed in Hamiltonian models of chaos.

Every node in a multi-agent large language model (LLM) workflow retrieves context from memory and injects it into its prompt, where those injected tokens are billed as input tokens at the same per-token price as the system prompt and the user query. Production observability tools report total token cost but do not separate the tokens a node generates from the tokens it is handed, so this component of the bill is invisible to the teams paying it. We introduce the Total Cost of Agency (TCA), a decomposition of multi-agent workflow cost into base prompt, inference, memory injection, miss penalty and context-accumulation components, and an exact attribution method: a two-pass, non-billable token count that measures injected tokens directly rather than estimating them from word-count proxies. On a 200-task enterprise benchmark executed against real model APIs, memory injection accounts for 13.6 percent of the variable cost a compile-time optimizer can act on, about 12 percent of the full billed cost, and its share rises from a structural zero at workflow depth one to 27.6 percent at depth six. Injected tokens grow linearly with depth over the measured range (R^2 = 0.9974, depths two through six); a quadratic fit yields a negative leading coefficient, so the data do not exhibit convex growth at these depths. We show the component is controllable at fixed model tier: reducing the retrieval window capacity from 32 to 2 entries lowers injected tokens by 28.7 percent with an accuracy change within seed-level variation. We report in full that our graph-rewriting transforms are approximately cost-neutral in isolation, that two of the five decomposition terms are zero by construction in this harness, and that total workflow cost is dominated by model tier assignment, which we hold fixed and treat as prior work. Prompt caching is not evaluated; all figures are for the uncached case.

Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.

The intricate procedure of mass renormalization in quantum field theory has a simpler precursor in classical electromagnetism. There, the renormalized mass of a charged body includes both its bare mass and its electromagnetic mass. For a body moving at constant low velocity, the electromagnetic mass can be calculated either from the total momentum of the electromagnetic field or from the total energy of the electromagnetic field in the body's rest frame. For a spherically symmetric charge distribution, these methods appear to disagree by a factor of 4/3. This 4/3 problem has a long history. Here, we see that the concept of field velocity can be used to quickly resolve the 4/3 problem. The two methods for finding the electromagnetic mass agree after noting that the average velocity of energy flow in the electromagnetic field is 4/3 the velocity of the body. The energy in the electromagnetic field moves faster than the charged body because, in addition to moving with the body, the field energy must make its way from the back of the body (where it is being emitted) to the front (where it is being absorbed).

A polarimeter does not report stress. It reports a retardance and an azimuth, and converting those to a stress pair fixes both the calibration that is required and the covariance that the subsequent inference must carry. We set out that observation chain for planar viscoelastic flow, combine it with velocimetry, and ask what the combined measurement can resolve. The calibration constant is fixed by three separately measurable quantities (path length, stress-optic coefficient and wavelength) rather than being fitted. Propagating the polarimetric errors to first order gives a stress covariance that is anisotropic and site dependent even for independent homoscedastic inputs, and whose conditioning degrades as the retardance approaches zero, where the linearization itself stops describing the measurement. Wrapping imposes a separate design bound. Two numerical studies follow, both in ideal calibrated stress coordinates under a prescribed covariance rather than the propagated polarimetric one. Holding the total scalar count fixed and varying the split between velocimetric and optical sites, an unequal allocation favoring optical sites outperforms either pure configuration. We then ask what the measurement resolves between constitutive models compatible with the same velocity data. In self-consistent pressure-driven flow of the finitely extensible nonlinear elastic Peterlin model, at extensibility L^2=50 and 3% noise, the optical channel rejects the velocity-compatible Oldroyd-B family in 78.1% of realizations at the Deborah number De=2, the ratio of the relaxation time to the flow timescale, and in 100% at De=4, while rejecting only about 5% below De=0.3. The resolving power of a design is therefore a strong function of Deborah number and must be quoted with it.

This paper presents a partial-scan-and-move strategy for source seeking with a mobile robot equipped with an offset scalar sensor. At each robot position, the sensor collects source field measurements while the robot rotates. Instead of requiring a complete circular scan before every move, we ask when the measurements collected over only part of the circle are already sufficient to determine the next action. We develop a gradient estimation method for partial scans together with a confidence set that accounts for measurement noise and local field variation. The robot uses this confidence set to decide whether it is close enough to the source or has enough information to move in a descent direction. We show that, under suitable conditions, each decision can be made within a prescribed partial scan and that the robot reaches a desired neighborhood of the source in finitely many moves with high probability.