Papers

We extend the quadrature method developed in [10] to Dirichlet $L$-functions associated with primitive characters. The approximations combine finite Dirichlet sums with correction terms whose quadrature coefficients can be precomputed for each character. Numerical experiments demonstrate high accuracy in the critical strip and in other vertical strips. We also describe how to combine these approximations with direct summation and Euler–Maclaurin summation to evaluate $L(s,\chi)$ throughout the complex plane.

Activation probes that monitor deployed language models are trained on synthetic conversations, and how many a probe needs is open. We trace learning curves over 10-590 synthetic samples for three monitoring concepts, high-stakes situations, replies harmful to a person, and replies that do not follow the user's instruction, on fourteen held-out evaluation distributions and four probe models, varying the generator LLM and the prompt's detail. The need is set by what is monitored: probes for high-stakes and harmful are within a few hundredths of their plateau from 80 samples on Gemma-3-27B-IT, instruction probes need several times as many, and the ordering holds on three smaller probe models and on real samples (from dev set). Prior work advises spending a generation budget on breadth, more kinds of data, over depth, more of each kind. We read the depth a concept needs as the half-gain size of a fitted curve, the number of samples at which half the gain is in hand. Concept and distribution account for 42-45% of its variance, the generator, probe model, and prompt detail for under 10%. What sets the value of the half-gain size is coverage, not per-kind difficulty: the number of samples of its own kind a distribution needs to saturate. Every kind, one per evaluation distribution, has a median half-gain size of 7-11 own-kind synthetic samples under all three concepts alike. What differs is how far samples of one kind transfer to the concept's other kinds, almost fully under high-stakes, less under harmful, and least under instruction, which accounts for most of the gap between concepts on generated and real samples. Breadth therefore pays differently by concept: many kinds are necessary under instruction, where no kind covers another, and nearly redundant under high-stakes, where one kind covers the rest. We release the evaluation suites, dev sets, and generated sets.

We present a new asymptotic matrix multiplication construction yielding $\omega<2.37115924$, and therefore an algorithm that multiplies two $n\times n$ matrices in $O(n^{2.37115924})$ arithmetic operations over the rationals, reals, or complex numbers. The construction improves the bound $2.371177$ of Dupont et al. within the combination-loss framework for the Coppersmith–Winograd tensor. Our approach combines a shared recursive parameter family with a conditioned optimization procedure that addresses two obstacles: weak gradients at low-mass constituents and competing bottlenecks in the retained exponent. A mass- and probability-dependent rescaling supports quasi-Newton optimization in $212\,820$ coordinates, while a six-control correction balances the three extraction roles at each relevant stage. Positive rational entropy-dual factors and an independent ordinary-string verifier turn the resulting construction into an exact certificate. The verified upper-bound expression lies in $[2.3711592385931075066123,\,2.3711592385931075066124]$. The complete witness and an offline verifier using only the Python standard library accompany the paper.

Historical Polish is well documented as a language but annotated in machine-readable form only to about a million words for the period this paper covers; the rest sits behind optical character recognition of variable quality. We present Wieszcz-XIX, a corpus of 6.75 billion tokens (about 3.1 billion words) in 294,369 documents, most of them periodical issues, of Polish published from 1800 to 1918, assembled from Wolne Lektury and the Internet Archive by a pipeline that filters, deduplicates, audits for post-1918 leakage and splits at the document level. It is over three orders of magnitude larger than the annotated corpus of the same period, and we quantify its defects: recognition corruption against a false-positive floor, near-identical duplication, which is removed, and post-1918 leakage, which is excluded from the training corpus itself down to a known residue of 0.04 to 0.38% of its bytes, found in the transcribed source, so the published corpus is the trained one document for document. On a hand-corrected sample the character error rate is 0.68% where the text is legible, and 45% of the sampled passages cannot be corrected. On it we train a ladder of decoder-only models from 47M to 349M parameters from scratch, and measure their temporal boundedness. Against two modern Polish base models, one far larger, the 349M shows a crossover, as does the 107M against the comparator of its size: post-1918 vocabulary costs them about 3.1 bits per byte more than period vocabulary, a gap the comparators do not show, and period vocabulary costs them fewer bits than it costs the comparators. Shown period text, the models keep its spelling and the comparators only partly. Adding parameters gains about twice as much as a second pass over the data. We release the corpus, code and weights. Content warning: the models reproduce period prejudice, including antisemitic statements.

In this paper, we associate a canonical topology with the transition operator of a discrete-time Markov chain. We prove that this construction defines an Alexandroff topology, called the Markov Accessibility Topology, and subsequently establish that it coincides with the Alexandroff topology induced by the accessibility relation. This establishes a direct connection between probabilistic accessibility and order-theoretic topology, allowing several classical notions from Markov chain theory to be interpreted in topological terms. Among other results, we characterize absorbing subsets as closed sets, relate irreducibility to topological connectedness and the triviality of the topology, describe minimal open neighborhoods through accessibility and hitting probabilities, and investigate the communication quotient together with its relationship to lumpability.

Tool-using agents repeatedly carry observations whose useful content can be much smaller than their original payload. We study agent-controlled forgetting: the acting model selects previously observed tool results, replaces each with a short note at its original position, and retains the exact original in a recoverable archive. A Python harness exposes batch archival and explicit recovery without task-specific model training, while protecting user instructions and assistant messages from these operations. In an exploratory OpenTelemetry debugging case followed by an unrelated implementation task, the method ended with 231,951 provider-reported prompt tokens versus 912,492 under retained history, used 50% fewer cumulative input tokens, and had an estimated API cost of USD 1.28-1.44 versus approximately USD 4.38. Both arms passed the two-case primary behavioral oracle; neither fully satisfied the follow-up evaluation. The method made more requests and took 17% longer. A contrasting application-development pair produced no context or cost saving, and an earlier continuation exhibited lower manually assessed quality despite reduced context. These observations demonstrate substantial resource savings in noisy tool-use trajectories and identify workload dependence as a central consideration for reversible context management.

We examine a Planck-scale regular black-hole remnant in neutron-star matter using a T-duality-inspired effective geometry and explicitly separate geometrical results from assumptions about absorption and emission. Within the static family, the surface-gravity temperature grows as $(M-M_{\rm ext})^{1/2}$ after a small mass increase. A constant-greybody Stefan–Boltzmann approximation gives a Hawking power proportional to $(M-M_{\rm ext})^2$ and can produce a stable lower balance point and an unstable growth threshold under stated hypotheses. For $l_0=\ell_{\rm Pl}$, however, the formal lower equilibrium has an excess mass of only $10^{-45}$–$10^{-46}\,\mathrm{kg}$ for order-unity absorption efficiency, so the canonical description is inconsistent with individual neutron captures. For a fiducial area-scale absorption cross section with unit coefficient, the mean capture interval is $5.4\times10^8\,\mathrm{yr}$ and the initial nonradiating growth timescale is $9.1\times10^{27}\,\mathrm{yr}$. Under this assumption, a Planck-mass remnant inside a neutron star is therefore effectively inert and, without additional feeding, cannot destroy the star within the age of the Universe. A stationary capture–relaxation state additionally requires an effective microscopic emission law; it is not established by zero temperature alone. Hydrodynamic accretion requires control of wave effects and a mean-free-path criterion; its onset corresponds to masses of order $10^{11}$–$10^{12}\,\mathrm{kg}$ for representative matter parameters. Direct zero-point-length corrections there are negligible, of order $10^{-40}$ at a femtometre. We discuss conditional growth thresholds, critical slowing near an unstable balance, dark-matter feeding, angular-momentum transfer, and the requirements for neutron-star survival constraints.

The existence of energy is the main criterion for (i) providing a common core to the materiality of all types of classical matter and (ii) denying that the gravitational field of General Relativity is a type of matter. Extending this criterion to quantum field theory, though formally straightforward, carries new conceptual consequences for the interpretation of gravity. Renormalization of the quantum matter stress-energy tensor forces a local, purely geometric term, built from the metric alone, into the conserved stress-energy, and this has two faces. It grants the metric a material significance alongside its spatio-temporal one (the egalitarian view); and it binds gravitational to non-gravitational energy so tightly that the two cannot be split apart without a choice of vacuum that a generic spacetime does not supply (the unificationist view). The latter poses a dilemma: either gravitational energy is meaningless, but then so is the energy of the non-gravitational quantum fields, and only classical fields remain matter; or both are meaningful, and the metric thereby acquires the material significance of a matter field. On neither horn does the classical divide between matter and spacetime survive quantization.

The Search for Extraterrestrial Intelligence programme aims to find evidence of extraterrestrial intelligence. SETI scientists pursue this objective by searching for technosignatures primarily in the radio or optical spectrum. The IAA SETI Committee has been developing protocols to offer guidelines in case of an actual extraterrestrial signal reception. These protocols establish procedures to confirm the authenticity of the signal and its actual extraterrestrial nature, as well as the committee's role in managing the discovery in relation to the scientific community and the general public, targeting scientific queries in relation to the management and development of equipment and methodologies employed in current SETI search. The project A Sign in Space part 2 aims to actively engage the global SETI community and the global telescope network, with scientific facilities responding and coordinating themselves to confirm the extraterrestrial nature of the received signal. The project develops some of the societal, scientific and technological methodologies already employed in the interdisciplinary work A Sign in Space. Here, we established a global collaboration between SETI scientists, radio observatories and the European Space Agency to test the communication and technological pipeline and protocols leading to the reception of a simulated extraterrestrial signal by a network of radio telescopes across the globe. We also employed an ESA spacecraft for system validation. A Sign in Space part 2 aims to further implement deep space technologies in SETI search through a structured and sustained programme, in collaboration with ESA, the SETI Institute and the Italian Institute for Astrophysics. The project will aim to stage and test the entire Post Detection procedure, implementing the protocol as envisioned by the IAA SETI committee.

For a symmetric subset of a group containing the identity, its universal local presentation records the multiplication relations visible within the subset. We prove that a group is recovered from every such generating subset if and only if it is trivial or cyclic of order two or three, as conjectured by P. A. Smith. The main step is an exact completion theorem: local maps into a target group always extend to generating domains if and only if every target element has a square root. By embedding an arbitrary group in a group with surjective squaring, we deduce that every partial local presentation embeds in a generating one. This gives subgroup inheritance and reduces the classification to finite generation. We also construct obstructions in one fixed countable metabelian target on domains of at most five elements. This bound is sharp even when the target is allowed to vary.

We investigate cosmological constraints on a $(3+1)$ neutrino framework containing an additional partially thermalized, eV-scale sterile neutrino alongside the three active species. Rather than assuming full thermalization, we allow the sterile abundance to vary independently through its physical mass $m_s$ and contribution $\Delta N_{\rm eff}$ to the effective number of relativistic species. The sterile state is modeled as a thermally distributed non-cold relic with a temperature below that of the active-neutrino background. We consider flat and non-flat $\Lambda$CDM and $w_0w_a$CDM cosmologies, all including the same $(3+1)\nu$ sector. The models are constrained using Planck 2018 CMB data, DESI DR2 BAO, Pantheon+ Type Ia supernovae, a conservative compilation of $f\sigma_8$ measurements, and the recent H0DN. Oscillation-informed priors are imposed on the active-neutrino mass splittings, while the eV scale sterile-mass range is motivated by short-baseline oscillation searches and global $(3+1)$ analyses. We find that allowing additional freedom in the late-time cosmological background substantially changes the inferred sterile-neutrino sector. The effective sterile mass increases from $m_{s,\rm eff}\sim0.11\pm0.05~{\rm eV}$ in flat $\Lambda$CDM$+(3+1)\nu$ to $\sim0.35\pm0.12~{\rm eV}$ in the non-flat $w_0w_a$CDM$+(3+1)\nu$ model. The corresponding sterile abundance shifts from $\Delta N_{\rm eff}\lesssim0.1$ to $\Delta N_{\rm eff}\simeq0.35\pm0.15$, while remaining well below the fully thermalized limit, $\Delta N_{\rm eff}\simeq1$. The non-flat $w_0w_a$CDM models also show $\sim 2.8\sigma$ preference for open spatial geometry, $\Omega_k\simeq0.0045\pm0.0016$, and yield $H_0\simeq70.9\pm0.7~{\rm km\,s^{-1}\,Mpc^{-1}}$ and $S_8\simeq0.785\pm0.015$. These models improve the minimum $\chi^2$ by approximately $21$-$25$ relative to flat $\Lambda$CDM$+(3+1)\nu$.

We give two explicit reformulations of a Balazard–Saias–Yor type criterion for the Riemann hypothesis. First, Jensen's formula is applied to $u(s)=(s-1)\zeta(s)$ after mapping the unit disk onto $Re s<1/2$. For the normalization whose center corresponds to $s=-1/2$, the images $z_n=(4n-1)/(4n+3)$ of the trivial zeros yield a telescoping Jensen product. This isolates, at finite radius, the complete divergent contribution of the trivial zeros; the remaining defect is a nonnegative integrated count of mapped nontrivial zeros off the critical line. A one-parameter version gives a gamma-quotient product and an explicit finite part. Second, after passing through the established boundary identity, we combine two Poisson weights to obtain an absolutely convergent logarithmic integral of the Riemann $\Xi$-function. From the random variable $Z=|\Xi(T)/\Xi(0)|^2$ we define its law $\mu$ and the size-biased law $\nu(\,\mathrm d z)=z\mu(\,\mathrm d z)/M$. The data-processing inequality is lossless for this statistic, and the Riemann hypothesis is equivalent to saturation of an explicit upper bound for $D_{\rm KL}(\mu\|\nu)$. We also record the associated Donsker–Varadhan and moment forms and express the target constant through Riemann's positive Fourier kernel. The analytic boundary criterion and Jensen–Hardy mechanism used here are known. The purpose of the paper is an explicit finite-radius treatment of the trivial zeros and an information-theoretic reformulation, not a new proof of the Riemann hypothesis or an independent boundary-integral criterion.

We give a complete local proof of Langlands's First Main Lemma for local epsilonfactors over nonarchimedean local fields. The proof builds on Dwork's p-adic calculations and Langlands's formulation of the local method. The present paper reformulates these calculations in a common normalization and extends the argument to equal characteristic. A more systematic treatment of stationary parameters and conductor cases is intended to make the calculations easier to follow. The author has also completed a local proof of Langlands's Second Main Lemma. Together with the present result and Langlands's remaining reductions, this gives a complete proof of the local construction of local epsilon factors envisioned by Langlands.

Let $p_n$ be the $n$th prime and $g_n=p_{n+1}-p_n$. Following Gafni and Tao, an integer $m$ with $p_n<m<p_{n+1}$ is rough for the gap if its least prime factor is at least $g_n$; let $M_n$ be the number of such integers. Gafni and Tao proved that the number of $n$ with $X\le p_n\le 2X$ and $M_n=0$ is $O(X/\log^2 X)$, and that it is asymptotic to $cX/\log^2 X$ under a form of the Dickson-Hardy-Littlewood prime tuples conjecture. We study $N_r(X)$, the number of $n$ with $X\le p_n\le 2X$ and $M_n<r$. For every $r\ge 1$ we define a constant $c_r$ by an endpoint-conditioned local sieve model, with $c_1=c$, and we prove unconditionally that $c_r=h_r^*+O_\varepsilon(r^{1/2}(\log r)^{1+\varepsilon})$ for $r\ge 3$, where $h_r^*$ is the least even $h\ge 2$ with $h\prod_{p<h}(1-1/p)\ge r$. Consequently $c_r=H_r(1+O(e^{-\kappa\sqrt{\log r}}))$ for an absolute constant $\kappa>0$, where $H_r>e$ solves $e^{-\gamma}H_r/\log H_r=r$ ($\gamma$ is Euler's constant), and $c_r=e^\gamma r(\log r+\log\log r+\gamma+(\log\log r+\gamma)/\log r+O((\log\log r)^2/(\log r)^2))$. The proof combines the Montgomery-Vaughan moment bounds for reduced residues in short intervals with an exact removal of the endpoint conditioning. For each fixed $r$, the argument of Gafni and Tao extends to give $N_r(X)\ll_r X/\log^2 X$ unconditionally, and $N_r(X)\sim c_rX/\log^2 X$ under their conjecture. Exact enumeration of the local model gives $c\ge 2.7413$.

In this paper, by using a signs rule for a class of special power series and a recurrence relation of coefficients involving hypergeometric series, we find the necessary and sufficient conditions for the sharp (at the left endpoint) inequalities between the hypergeometric function and power mean (Hm-Pm inequality) to hold in all possible cases, which greatly extends those known results and solve the rest of problem on the sharp (at the left endpoint) power mean bounds for the hypergeometric mean.

Large language models (LLMs) are increasingly being integrated into hardware verification to automate specification interpretation, verification-artifact generation, debugging, formal reasoning, and tool orchestration. This survey provides a systematic review of LLM-assisted hardware functional verification across SystemVerilog assertion generation, stimulus and testbench generation, bug localization and design repair, model checking and equivalence checking, SAT/SMT optimization, and emerging agentic verification workflows. We organize the literature by methodology, verification objective, tool interaction, benchmark, and evaluation criterion, and examine both inference-time techniques–including prompting, retrieval, structured reasoning, and agentic workflows–and training-time adaptation. Across these areas, a common pattern emerges: LLMs are most effective as semantic reasoning, search, and orchestration components embedded within verification-aware workflows, while simulators, formal engines, coverage tools, and solvers provide executable feedback and correctness evidence. However, tool acceptance alone does not establish verification correctness, since assertions, tests, repairs, or proofs may satisfy available checks without faithfully capturing the complete design intent. We therefore identify semantic alignment between specifications and verification evidence, scalable integration with deterministic tools, generalization to unseen designs, and rigorous evaluation of correctness, cost, robustness, and human effort as key challenges. Finally, we discuss emerging directions toward specification-centered, neuro-symbolic, and persistent agentic verification systems that combine LLM flexibility with independently checkable verification evidence.

When computing tree-level amplitudes of the nonlinear sigma model (NLSM) via the BCFW on-shell recursion relation, boundary terms are inevitable. Here, the BCFW recursion relation refers to the original prescription with momentum-shifts on two external legs, as opposed to the generalized versions with redefined momentum-shifts. We propose a simple general scheme that determines the boundary terms of NLSM amplitudes recursively from lower-point amplitudes. Hidden zeros and mass dimensions severely constrain boundary terms, allowing us to compute these terms from the $2$-split property of the tree amplitudes. Combined with the existing rules in the literature for obtaining the two currents in the $2$-split from on-shell amplitudes, this scheme enables the recursive construction of boundary terms for higher-point amplitudes from lower-point amplitudes.

Scientific studies of language agents need behavioral variables that support hypotheses across tasks and models. We formulate this research problem as learning and testing a hierarchy of trajectory abstractions. A concrete recursive procedure first measures role- and phase-indexed events, proposes temporally constrained relations, and tests their stability across conditions. It then constructs episode-level motif variables from selected relations and repeats the analysis on those variables. Explicit measurement functions connect every abstraction level to the original trajectories. Observations and randomized protocol experiments assess the resulting hypotheses, while comparisons between intervention realizations determine whether an abstraction should be retained, refined, or restricted. We derive a finite-depth bound for accepted reductions, identify protocol effects on fixed abstractions, and characterize realization disagreement and composition of abstraction error. A finite-sample test makes projected intervention consistency operational, and constructed examples illustrate motif construction and abstraction refinement. The formulation distinguishes this experimental approach from semantic taxonomies, qualitative theory induction, and behavior-model recovery. It specifies a proposed research procedure for discovering generalizable behavioral hypotheses, with literature-relative novelty assessed separately from model-relative surprise.

A recent ALICE measurement reports a finite strangeness enhancement in the toward-leading region of high-multiplicity proton-proton collisions. In this work, the trigger transverse momentum, $p_{\rm T}^{\rm trigg}$, dependence is investigated using ${\rm K}^{0}_{\rm S}$ and $\Xi^{\pm}$ production in PYTHIA8, with and without color ropes, and EPOS-LHC. For $3 < p_{\rm T}^{\rm trigg} < 15$~GeV/$c$, EPOS-LHC and PYTHIA8 with color ropes exhibit a multiplicity-dependent increase of the toward-leading $\Xi^{\pm}/{\rm K}^{0}_{\rm S}$ ratio, while the rope-free PYTHIA8 baseline shows a weaker dependence. With increasing trigger momentum, the enhancement is strongly suppressed in EPOS-LHC for $p_{\rm T}^{\rm trigg}\gtrsim10$~GeV/$c$, whereas it remains approximately unchanged in PYTHIA8 with color ropes. This contrasting behavior is consistent with a reduced core contribution in EPOS-LHC and a local string-overlap mechanism in PYTHIA8 with color ropes. The trigger transverse momentum thus provides a model-sensitive probe of the mechanisms contributing to the apparent strangeness enhancement in the jet-like region of the pp collisions.

The problem of incompressible fluid mixing is long-studied, yet many questions remain open. This paper aims to address the question “what do efficient flow fields for mixing look like, and how do they behave?” Inspired by the dynamic and geometric approach to optimal mass transport, we formulate a version of the fluid mixing problem as an optimal control problem for transport of a passive scalar, in which the dynamics are given by the continuity equation together with an incompressibility constraint. We then develop a geometric framework around this problem which parallels that of classical optimal transport: the optimal control problem induces a metric on the set of reachable states (analogous to the Wasserstein metric), and this metric carries a formal Riemannian structure when the optimal control objective is induced by an inner product. Using this structure, we decompose our problem into a series of more fundamental geometric problems and derive (formal) necessary conditions for optimality, geodesic equations, and gradient flows for mixing. Specializing the control objective to the kinetic energy recovers the incompressible Euler equation, connecting our framework to the geometric hydrodynamics of Arnold. The resulting problem appears to be ill-posed, however, suggesting that the kinetic energy is an unnatural measure of mixing effort. Specializing instead to the enstrophy, which we argue is better suited to mixing, yields the Euler-Poincaré (EPDiff) geodesic equation for the right-invariant homogeneous $\dot{H}^1$ metric on the group of volume-preserving diffeomorphisms, and we present numerical simulations of both geodesics and gradient flows in this case. Along the way, we generalize the classical Helmholtz decomposition of vector fields, rederive the Clebsch representation of incompressible flows, and develop a parallel to the Otto calculus of optimal transport.

Longitudinal observational data are often subject to informative missingness. For example, in healthcare research using electronic health records, covariates and outcomes are measured only when patients interact with the healthcare system. Whether these data are observed usually depends on the unobserved variable values themselves, introducing a common form of data missing not at random. We develop identification and estimation methods for the effects of longitudinal modified treatment policies under a self-censoring model which explicitly models this dependence. We consider effects of treatments that can be modified only at measurement times (e.g., interactions with the heathcare system). We study two settings: one in which the observed history suffices for treatment confounding control, and another in which confounder control requires covariate values that were not measured at missed visits. In both settings, we combine longitudinal causal identification with shadow-variable conditional moment restrictions to obtain recursive identification formulas for the counterfactual outcome mean. We derive gradients of the pathwise derivatives and second-order remainder expansions, and use these results to construct estimators that accommodate machine learning for nuisance-function estimation. Under suitable product-rate conditions and cross-fitting, the estimators are asymptotically linear and permit root-n inference, including simultaneous inference across outcome times. We also describe conditional-moment learning and ensemble approaches for estimating the nuisance functions required by our approach, together with a pool-and-smooth strategy that borrows information across sparsely measured outcomes.

We prove conditional lower bounds for approximating dynamic time warping (DTW) over the uniform metric on three symbols. Let $N, M$ be the two string lengths and $n, m$ their respective numbers of runs. Under the Gap Block Disjointness (GBD) hypothesis, for every fixed $\kappa \in (0,1/6)$ and $\delta \in (0,1)$, no deterministic algorithm $N^{\kappa\delta}$-approximates DTW on two explicit strings of length $N$ in $O(N^{2-\delta})$ time. This matches the known tradeoff between approximation and running-time exponents for deterministic algorithms within any fixed factor greater than six in the approximation exponent. For run-length encoded strings, the Orthogonal Vectors Hypothesis (OVH) rules out any constant-factor approximation in $\widetilde{O}((nm)^{1-\delta})$ time for every constant $\delta>0$. More generally, for every fixed $\eta \in (0,1)$, it rules out $(N+M)^{1-\eta}$-approximation in the same running time. These bounds extend to every fixed metric with at least three points, including absolute distance on $\{0,1,2\}$. Both reductions use long runs to force equal-symbol matches in low-cost alignments. For explicit strings, we combine Boolean gadgets with deterministic gap amplification to obtain a polynomial approximation gap. For run-length encoded strings, an encoding of regular-expression membership gives accepting instances an alignment whose cost does not increase as selected runs grow. Rejecting instances have distance at least the chosen run length, while the number of runs stays fixed.

Achieving nanoscale light confinement and long-range propagation is a central challenge in nanophotonics, with important implications for controlling molecular photophysical processes and energy transfer. Monolayer transition-metal dichalcogenides (TMDs) support in-plane exciton-polaritons (IPEPs), deeply subwavelength optical modes in the visible range. In this regime, electromagnetic fields vary on length scales comparable to the exciton size, making spatial nonlocality in the excitonic optical response essential. Here, we develop a microscopic theory of the nonlocal excitonic optical response and investigate the near-field properties of IPEPs in hexagonal boron nitride (hBN)-encapsulated monolayer WS$_2$. Combining a two-band massive Dirac fermion description with a generalized Mott-Wannier treatment, we derive a nonlocal electric susceptibility that accounts for both the center-of-mass and internal relative motion of excitons. Spatial nonlocality in the excitonic optical response shifts the polariton dispersion toward lower in-plane wavevectors compared with the results based on the local-response approximation. This reduces high-wavevector contributions and produces smoother near-field distributions that extend over larger lateral distances while retaining nanoscale confinement. Furthermore, at higher excitation energies, multiple exciton-polariton modes contribute at distinct wavevectors, and their relative contributions can be tuned by varying the thickness of the capping hBN layer. These insights elucidate the fundamental role of spatial nonlocality in the polaritonic properties of van der Waals heterostructures.

Uncertainty quantification in machine learning models is essential for nuclear energy applications. While machine learning models can make both uncertainty and point predictions, these models are often significantly more difficult to train jointly than models that make point predictions alone. Split conformal prediction is a family of methods for computing distribution-free prediction intervals by calculating nonconformity scores corresponding to a target quantile in a calibration dataset. Although conformal prediction only guarantees marginal coverage, normalizing nonconformity scores enables predictive interval widths to be calculated on a per-sample basis, providing an approximation to conditional coverage. In this work, we connect uncertainty predicting neural networks to pre-trained networks that estimate shielding factors in multigroup neutron cross sections. We train the uncertainty models on the same OpenMC data used by the pre-trained models, whose weights and biases remain fixed. The outputs of the uncertainty models are the standard deviations of the residual, separated into contributions from the model and tally uncertainty. Their corresponding variances are combined in quadrature to provide a normalizing factor for conformal prediction, providing interval widths that are adaptive on a per-sample basis. Baselines for comparison are established using Mondrian conformal prediction, and by using the ground truth OpenMC uncertainties as normalizers in the conformal framework. We use predicted uncertainty interval widths and the severity of predictions that overshoot the interval widths as bases for comparing our normalizer with the baselines. We find that our method dramatically reduces both interval widths and the degree to which predictions fall outside these widths.

Partial identification (PI) entails estimating bounds on causal effects by encoding different assumptions on data generation as a constrained optimization problem. Such bounds can suffice to inform policy decisions even if the causal effect itself is not identifiable. Often vacuous in practice, practitioners seek to exhaustively encode domain knowledge as additional constraints to make the PI bounds more informative. We introduce known data symmetries – invariance of the causal effect under certain data transformations – as a new source of constraints to inform PI. We operationalize this as a shape constraint on the causal function, and via a change of measure against which PI is posed using simple data pre-processing. Both approaches are shown to sharpen bounds under two canonical PI models. This is shown both theoretically for the population case, and via experiments in the finite-sample case. More broadly, our framework establishes data symmetries as a natural, underutilized source of background knowledge for robust causal inference.

LLM-as-judge is now a standard tool for scalable evaluation, but judge performance is still often summarized by a single accuracy number. This aggregate view hides the deployment conditions under which a judge succeeds or fails. We introduce Conditional Accuracy Profiling (CAP), a post-hoc diagnostic framework that decomposes pairwise LLM-judge accuracy into eight conditions organized into content sensitivity, robustness, and rationale quality. CAP is benchmark-agnostic: it can be applied directly when a benchmark provides the required annotations, approximately through task-subset proxies, or through controlled augmentation when perturbation pairs can be generated. We instantiate CAP on seven LLM judges across six pairwise judging benchmarks, including judgerEva-Standard, a controlled testbed we created to support all eight conditions. CAP exposes profile differences hidden by aggregate accuracy: on judgerEva's judge-independent Hard-Constructed subset, the two judges most sensitive to omitted qualifications rank in the bottom three of seven by overall accuracy, so omission sensitivity is not predicted by aggregate accuracy. Across benchmarks, Position Robustness shows the strongest rank stability (mean Spearman $\bar{\rho}{=}0.87$) but is itself fragile under JudgeBench-Pro adversarial stress, showing the largest mean accuracy drop among the shared conditions, though the dominant degradation channel varies by judge. Condition-level profiles provide a more actionable basis than aggregate accuracy for selecting LLM judges.

Vision-language-action (VLA) policies trained on large datasets are capable within their training domains, yet they still fail to generalize to the variety of situations a robot meets in real-world deployment. Agentic robot systems complement the policy with a vision-language model (VLM) orchestrator that learns when to call the policy, how to instruct it, and when to use scripted skills instead. However, because the harness is built around a frozen policy that has limited language steerability, the orchestrator can avoid the policy's failures but never overcome them. The policy becomes the bottleneck of the whole system. Fine-tuning the policy can remove this bottleneck, but updating it alone decouples it from an orchestrator tuned to its old behavior. We propose Robo-COP, in which the orchestrator and policy co-evolve during deployment. Robo-COP curates skill demonstrations from its own executions, fine-tunes the policy when this data can address recurring failures, and adopts each new policy only after it improves the skills it was trained for. Across ten simulated RoboLab tasks, Robo-COP raises mean held-out success from 64.8% to 73.8% over the same harness with a frozen policy, while fine-tuning on a fixed schedule without verification reaches only 65.8%. On three real-world tasks, Robo-COP raises held-out success from 38.3% to 50.0%. Robo-COP turns deployment into a self-improving flywheel in which robots learn by doing, with each improvement in execution producing better data for the next round of learning. Videos and code are available at https://robo-cop.pages.dev/.

Mixed-precision post-training quantization needs a per-module sensitivity signal; for a text embedder the obvious one – the retrieval quality a module costs when quantized – needs relevance labels that deployments rarely have. We measure a label-free substitute: quantization-induced representation drift, obtained by quantizing one module, re-encoding the corpus, and recording how far the output embeddings moved from their full-precision positions. What is specific is the observable: the deployed output representation a dense retriever ranks with. Across five development embedders, configuration-level drift orders sampled mixed-precision plans against held-out retrieval quality at a macro Spearman of 0.911, the sensitivity transports across calibration corpora and retrieval domains in the usable regime, module drifts compose rank-consistently but not numerically, and relevance-derived sensitivity adds no consistent value. The method is one additive allocation under a hard packed-byte budget, with no labels and no search. On three embedders held untouched until method, baselines and hypotheses were frozen and sealed, the pre-registered directional hypothesis against the prior LieQ criterion holds (3/3 at the main budget, no collapse) and drift scores above a two-sided LieQ steelman in 2/3; but at the main budget drift is numerically lower than same-budget uniform precision on all three (-0.99, -0.85, -1.01 points), having reduced module and whole-model drift as designed. Output drift is thus a robust coarse sensitivity signal, not a universally optimal allocation objective: it avoids the catastrophic failures of the transferred signed-geometry adaptation and can remain usable at stressed budgets where uniform collapses, but fine-grained redistribution around a strong uniform operating point remains unresolved.

Data collection using Unmanned Aerial Vehicles (UAVs) is challenging when LoRa IoT Devices (IoTDs) duty-cycle to conserve battery. Under energy constraints, a UAV must decide which IoTDs to visit, in what order, where to hover, and how many times to probe each node, while time-based data freshness decays. Tractably solving this problem requires a multi-level optimization architecture: discrete combinatorial optimization for routing, continuous global optimization for spatial positioning, and sequential decision-making under uncertainty. We propose FLoRa, a Flight-assisted LoRa data collection architecture using Simulated Annealing (SA) for path planning, Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for hover positioning, and Partially Observable Markov Decision Processes (POMDPs) for probing IoTDs. To quantify collection utility from duty-cycling nodes, we introduce the Value of Information for Pull-based systems (VIP), a metric that rewards fresh data and penalizes failed probes, imposing well-posedness and preventing indefinite probing when an IoTD is off. Tracking hard battery constraints on every POMDP sample path requires state augmentation, worsening the curse of dimensionality. For tractability, SA and CMA-ES work on the hard battery constraints, while at the POMDP layer we relax them into soft average constraints via Lagrangian relaxation. Since solving the network-wide POMDP is computationally complex, we decompose it into node-level POMDPs by approximating inter-node time dependency using a forward-decomposition technique. Evaluation shows FLoRa outperforms metaheuristic, greedy, and deep reinforcement learning baselines by 30.6%, 27.8%, and 15.2% in total expected VIP, while increasing node coverage by 24.5%, 29.2%, and 8.8%, and successful collections by 24.3%, 25.6%, and 15.2%, respectively.

Electromyography-to-Speech (ETS) synthesis is typically a non-linear, chaotic dynamical system. However, no prior work has studied the chaotic behavior of ETS synthesis to date. Yet, prior works strictly rely on standard reconstruction metrics with parameter-heavy transformers that systematically over-smooth natural acoustic dynamics. To close this gap, for the first time, we propose a chaos-inspired Lyapunov-derived activation function (LyRIC) with two novel chaotic loss functions, Lyapunov Exponent Regularization and Multi-Scale Detrended Fluctuation Analysis, to explicitly capture the deterministic chaos of human phonation. In addition, we introduce a compressed novel encoder, GLAME, which synergizes global Mamba state-space modeling with localized GLARE attention. We comprehensively perform frame-level acoustic evaluation in a multilingual and multi-speaker setup using English and Mandarin datasets. The proposed system outperforms the established baseline with a 4.69x increase in objective intelligibility (STOI: 0.61 vs. 0.13) and a 2.08x improvement in spectral reconstruction (LSD: 1.08 vs. 2.25). Importantly, this improvement is achieved with 73.49% fewer parameters (14.34M vs. 54.10M), establishing a new baseline for ETS synthesis. To the best of our knowledge, this is the first work demonstrating that integrating non-linear chaotic physics into neural networks yields superior yet compact inductive biases for real-time ETS synthesis.