Inferring the sign of social relationships from online interactions is a fundamental challenge in social network analysis. Existing approaches typically rely on sentiment analysis to label individual interactions as positive or negative, then aggregate these labels to assign a sign to the relationship. However, sentiment analysis captures the valence of the content being discussed rather than the nature of the relational exchange itself, a conflation that can lead to systematic misclassification. In this paper, we propose a methodology that addresses this limitation by leveraging Large Language Models (LLMs) in a zero-shot setting to identify interaction-level relational signals (specifically, personal praise and personal attacks directed at the interlocutor) as more direct indicators of positive and negative social ties. We evaluate four models spanning open-weight and proprietary architectures (Qwen2.5:7b, Gemma2:9b, GPT-4o, GPT-5.4-mini) across three prompt designs of increasing complexity, on two human-annotated datasets of approximately 298 and 340 texts respectively. Results show that zero-shot LLMs achieve good classification performance on both tasks without any task-specific training data, establishing a practical baseline for relational annotation. Performance differs across tasks: attack detection is robust to prompt design and model choice, while praise detection is more sensitive to both, reflecting the greater subjectivity of positive relational gestures. These findings lay the groundwork for integrating LLM-based relational annotation into sign prediction pipelines.

Anti-computational arguments show that externally imposed computational interpretations cannot ground consciousness, but they do not establish that all computational organisations are observer-relative. We develop intrinsic computational functionalism: the view that, if consciousness is computationally constituted, it depends on physically realised computational structures the system has in virtue of itself rather than on labels imposed by an external interpreter. Two criteria operationalise this view. (C1) System-intrinsic instantiation: the relevant property must be specifiable without an observer's labelling, and invariant under structure-preserving relabellings of the system's variables. (C2) Causal-dynamical organisation under intervention: the property must be grounded in a state-space structure whose variables mutually constrain one another, and whose organisation is exhibited in counterfactual response under intervention. Together these criteria specify what any candidate computational account must satisfy to remain observer-independent, without selecting which intrinsic structures bear on experience. The argumentative core is a three-tier decomposition of identification work: interpreter-relative label selection (tier i), theoretically constrained partition selection (tier ii), and dynamics-internal grain selection (tier iii). We argue that any computational property capable of avoiding the observer-relativity objection must be identified, if at all, through tier (iii) dynamics-internal grain selection, conditional on empirically disciplined tier (ii) choices. Syntax-is-not-semantics arguments, mapmaker arguments, and the observer-relativity component of biological-naturalist objections succeed against views that locate the consciousness-relevant property at tier (i); once the tiers are distinguished, intrinsic computational functionalism survives.

The goal of this article is to show the categorical links between on the one hand the category of reductive Lie algebra pairs $\mathcal{RLP}$ and on the other hand the category of Lie-Yamaguti algebras $\mathcal{LY}$. The fact that the well-known construction of an enveloping algebra associating to a Lie-Yamaguti algebra a reductive Lie algebra pair is not functorial leads us to the main construction of the article, namely a left adjoint to the natural restriction functor $G:\mathcal{RLP}\to\mathcal{LY}$. As a final result we observe that the construction of the enveloping algebra becomes functorial when one restricts the morphisms of the categories $\mathcal{RLP}$ and $\mathcal{LY}$ to the surjective ones. Then it becomes a right adjoint to the restriction functor.

We present a novel approach to eigenvector universality for generalized Wigner matrices. Our main consequences are asymptotic normality of joint eigenvector projections everywhere in the spectrum as well as a quantitative lower bound on the largest entry of an eigenvector. In the case of smooth entries, we are able to obtain joint normality of an explicit growing number of eigenvector projections, and we are also able to obtain an explicit rate of convergence in Kolmogorov distance. This is based on a new analysis of the Dyson vector flow which does not rely on the eigenvector moment flow.

Polymers are indispensable materials with applications ranging from electronics to medicine owing to their versatility, which can be tailored by adjusting their chemical composition and architecture. The design space for these compounds is vast and governed by factors such as monomer classes, copolymer configurations (e.g., linear, branched, random, and alternating), chain size, stoichiometry, and material properties (e.g., density, refractive index, solubility, and Poisson's ratio). Exploring this space requires efficient computational methodologies for polymer science. To address this challenge, we introduce PolyGraphPy, an open-source Python framework that integrates atomistic simulations with machine learning for accurate property prediction and property-guided polymer design. The framework automates Density Functional Tight Binding calculations to efficiently construct structured datasets for monomers, homopolymers, and alternating copolymers. For property prediction, PolyGraphPy employs Bayesian Graph Neural Networks (GNNs) with stochastic graph representations to predict target properties, such as static polarizability, while providing robust uncertainty quantification. Furthermore, the platform incorporates two complementary generative models for the de novo design of targeted molecules: a SELFIES-based Generative Pretrained Transformer (GPT) and a Genetic Algorithm (GA) based on BRICS graph fragmentation. Demonstrated on a dataset of acrylates, PolyGraphPy provides a highly customizable end-to-end pipeline that reduces computational costs and accelerates data-driven polymer informatics.

We present a comparative study of four supervised machine learning regression algorithms -- Support Vector Regression (SVR), Gradient Boosting Regression (GBR), Gaussian Process Regression (GPR), and Multilayer Perceptron (MLP) -- for predicting the proton structure function $F_2^p(x, Q^2)$ using high-precision BCDMS experimental data. Unlike conventional methods that solve the DGLAP evolution equations, our data-driven framework directly captures the complex nonlinear dynamics of partonic structure. To ensure statistical robustness, we employ $k$-fold cross-validation and perform thorough hyperparameter optimization. Our results show that the MLP and GPR models achieve superior predictive accuracy. In particular, MLP exhibits the highest sensitivity to nonlinear gradients, while SVR proves most stable against experimental uncertainties. The close convergence of training and validation metrics confirms that the models learn the underlying QCD physics without overfitting to statistical fluctuations. This work highlights the potential of ML-based regression as a complementary tool for structure function analysis and kinematic extrapolation in high-energy physics.

We model a market with multiple dealers who compete for client order flow by dynamically updating their bid and ask quotes for a risky asset. Dealers aim to maximise expected profits while controlling inventory risk by skewing their quotes to attract offsetting order flow (internalisation) or by directly offloading positions in the market (externalisation). Using a variational approach, we derive a closed-form equilibrium for the resulting Nash competition, shedding light on key features of dealer market dynamics. We show that dealers relying on internalisation are compelled to increase their externalisation activity when competing with externalising dealers. This strategic shift in equilibrium leads to significantly higher hedging costs for all dealers and substantially wider spreads for clients.

We formulate stationary-density-preserving nonreversible perturbations of Fokker--Planck dynamics as gauge fields that deform relaxation spectra while leaving the invariant state fixed. When detailed balance holds, a similarity transformation maps the reversible Fokker--Planck operator to a Witten-Laplacian-type supersymmetric Hamiltonian; nonreversible gauges then appear as non-Hermitian perturbations that preserve the zero mode but modify the excited spectrum. This operator viewpoint gives a common language for relaxation gaps, circulating probability currents, hypocoercive acceleration, and finite control costs. We represent admissible gauge currents by antisymmetric tensor fields and identify the detailed-balance-violating Ohzeki--Ichiki force as a constant symplectic example whose infinite-strength limit is Hamiltonian dynamics. The continuous-time spectral gap alone does not select a finite gauge strength, so we introduce a finite-time regularized objective and an actor--critic procedure for learning the gauge. An exactly solvable anisotropic Gaussian Ornstein--Uhlenbeck benchmark separates the spectral transition from the finite-time optimum and shows that the learned gauge recovers the Lyapunov-equation optimum. A double-well benchmark then illustrates the same constrained selection in a nonconvex metastable landscape. Stochastic gradient methods enter this framework as physically relevant Fokker--Planck systems: mini-batch noise acts as an effective diffusion tensor, and adaptive methods such as Adam correspond to metric choices with possible nonequilibrium currents.

Concordance indices are widely popular metrics for assessing the ability of predictive survival models to discriminate underlying risk levels. However, these statistics have also been criticized for using only the rank orderings of the model's predicted risk scores and being insensitive to important model features, such as the addition of strong predictor variables into the model. In this paper, we address these limitations by developing smooth concordance metrics that model the underlying risk discrimination probabilities as continuous functions of the predicted risk score differences, where the shapes of these functions are estimated from the observed data. As a result, these smooth concordance metrics assess model performance across the entire range of possible risk score differences, allowing one to identify specific scenarios where the candidate model performs especially well or better than other models. Simulations show that the proposed smooth concordance metrics provide more detailed information about risk discrimination performance and are much more sensitive to the addition of meaningful predictors. We apply these methods to compare predictive survival models for cancer recurrence.

Ultralight axions (ULAs) are well-motivated dark matter particle candidates that arise in many extensions of the Standard Model of particle physics. ULAs with mass $m_\mathrm{a} \lesssim 10^{-27}$ eV have been strongly constrained by cosmic microwave background (CMB) observations in temperature and polarization. We fit recent measurements of gravitational lensing of the CMB from \textit{Planck}, the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT-3G) using a state-of-the-art simulation-calibrated nonlinear clustering model for ULAs. We derive the strongest constraints on ULAs in the mass range $10^{-26}\;\mathrm{eV}\leq m_\mathrm{a}\leq 10^{-24.5}\;\mathrm{eV}$. ULAs of this mass have been shown to alleviate tensions between inferences of the matter clustering if they compose a few percent of the total dark matter content of the Universe. We conclude that ULAs with a mass of $10^{-26}$ eV make up less than 1.5\% of the dark matter and $10^{-25}$ eV axions make less than 9\% (both at 95\% confidence level). We identify a slight preference for non-zero axion density at $10^{-24.5}$ eV at $2.1σ$. We find that the preference for ULAs is largely driven by a few data points and that further investigation of non-linear ULA physics is needed to confirm or rule out this signal.

While core-collapse supernovae have been widely discussed as potential neutrino sources, definitive observational evidence has remained elusive. In this work, we report evidence of high-energy neutrino emission in the direction of supernova SN 2021foa, which is one of the closest and brightest interacting supernovae observed to date. Using the second data release of muon track data from the IceCube Neutrino Observatory, we conducted a time-dependent analysis and identified a neutrino clustering that temporally coincides with the optical peak of SN 2021foa, occurring approximately 16 to 22 days after the discovery date, with a maximum test statistic of $\sim 28.2$. Monte Carlo simulations indicate that the probability of observing such a neutrino excess by chance is $\sim6.7 \times 10^{-5}$, corresponding to a significance of $\sim4.0\,σ$. The spatial and temporal correlation strongly suggests that the neutrinos originate from the supernova. SN 2021foa is a unique "flip-flop" supernova; its spectra repeatedly transitioned between hydrogen-rich (Type IIn) and helium-rich (Type Ibn) phases within 50 days post-peak, reflecting a violent and complex mass-loss history of its progenitor. The inferred neutrino energy exceeds the optical radiative energy and ejecta kinetic energy of the supernova by orders of magnitude, suggesting that the neutrino emission is likely powered by a delayed central engine driving a jet that is choked within the dense circumstellar medium.

This study presents a novel framework for estimating the central sea-level pressure ($P_{\rm c}$) of tropical cyclones (TCs) using infrared radiometers. We leverage the long-overlooked combination of high spatial resolution and sounding capability of the Moderate Resolution Imaging Spectroradiometer (MODIS) to measure warm-core anomalies in TC eyes. We develop the MODIS Thermal Infrared Sounding (MOTIS) framework, which performs instrument-specific preprocessing and estimates $P_{\rm c}$ using multiple linear regression. MOTIS yields $r^2 = 0.945$ and RMSE = 4.3 hPa for high-intensity TCs ($\overline{P}_{\rm c} = 937$ hPa) with clear eyes observed, outperforming all existing methods for intense TCs. We construct a dataset of 3288 (1082 clear-eye) MOTIS estimates from 2002 to 2025 and demonstrate its potential to improve the quality of Best Track $P_{\rm c}$, roughly halving uncertainties in the absence of pressure observations. Although MODIS is nearing the end of its mission, the MOTIS framework could be extended to next-generation geostationary sounders to provide accurate real-time $P_{\rm c}$ estimation for high-intensity TCs.

This paper studies expected $\mathcal{L}_2$ string stability of event-triggered vehicle platoons in which a human driver leads a chain of cooperatively controlled autonomous followers under stochastic communication delays. The leader's driving behavior propagates through the string via vehicle-to-vehicle (V2V) communication, so human-induced disturbances must not amplify along the platoon. Unlike deterministic approaches based on worst-case delay bounds, we derive string-stability conditions depending on the full delay distribution through integral inequalities. The closed-loop platoon is modeled as a stochastic hybrid system capturing vehicle dynamics, communication events, and event-triggering. This framework certifies string stability even when delays exceed deterministic admissible bounds with nonzero probability. Results are evaluated under several delay distributions using the MATLAB HyEQ simulator.

Engineering design is an iterative, simulation-driven process where traditional workflows rely heavily on computationally expensive analyses such as finite element and computational fluid dynamics. Although data-driven methods have accelerated design evaluation and optimization, most existing geometric representations discard parametric and feature-level semantics, limiting their integration with CAD-driven design workflows and reducing model interpretability. To address this gap, this work introduces Attributed Feature Graphs (AFGs), a feature-based representation that encodes design features, such as extrusions, ribs, and pockets, as nodes and their geometric or dependency relations as directed edges. AFGs preserve design intent and parametric structure while remaining compatible with standard graph-based learning methods, enabling end-to-end learning directly on CAD-derived feature graphs. The paper demonstrates the proposed representation through a surrogate-modeling case study on the CarHoods10K automotive hood frame dataset, where a Graph Neural Network (GNN) is trained as an evaluation engine to predict performance metrics from AFG inputs. The learned model achieves competitive surrogate performance compared with traditional data-driven approaches, but with the added benefit that engineers can map predictions back to specific CAD features and interpret how individual design elements influence system behavior. Furthermore, because AFGs are built from native CAD features, engineers can directly edit the underlying geometry in the CAD environment and reevaluate the design through the same learned model.

We propose a resolution of the firewall paradox in JT gravity by incorporating topology change into canonical quantization under relational time evolution. The gravitational Hamiltonian acts on the black hole interior through a pair of pants interaction, mapping between a single interior sector and a connected two interior sector. To describe dynamics in the interior while keeping track of the exterior, we pass to an extended phase space description obtained by splitting the bulk Hilbert space across the event horizon. The split introduces boost edge modes at the horizon, which the Hawking modes become gravitationally dressed to. Covariance of the resulting crossed product algebra provides a precise gravitational realization of the firewall: a one sided boost of the interior edge mode relative to the exterior holding the matter fixed, or equivalently, a relative phase between the interior and exterior Hawking partners holding the edge modes fixed. Although each topology changing transition is exponentially suppressed, evolution over a Page time causes the connected two interior branch to dominate. One of these is the naive semiclassical interior, which we show carries a nontrivial one sided boost upon gluing the interior back to the exterior, and hence a firewall. The other interior is shown to be a zero mode of the one sided boost generator. Gluing the interior back to the exterior quotients by the gravitational constraints, which annihilates the firewall branch. On the surviving branch, we show the horizon vacuum measurement and the early radiation purity measurement become the same Dirac observable. Equivalently, we show that Page time dynamics induces a large diffeomorphism on the connected branch under which the operator algebra of the interior Hawking partner and that of the decoded early radiation are identified.

Lens spaces are useful test examples in spectral geometry because their spin Dirac eigenspaces admit explicit congruence descriptions. We use these descriptions to study equivariant $η$ invariants for three-dimensional lens spaces with the round metric and the standard coordinate-torus action, retaining the spin-Fourier character of each eigenspace rather than only the ordinary scalar $η$ value. For the square family $L(\ell^2,\ell-1)$ and $L(\ell^2,2\ell-1)$, with $\ell\geq 5$ odd, we obtain a residual-circle equivariant $η$ separation: the ordinary $η$ values agree, and the first derivative of the residual $η$ germ vanishes by symmetry, but the second derivative is nonzero. For $L(25,4)$ versus $L(25,9)$, the normalized second derivative is $-6080$. Thus, the residual-circle equivariant $η$ germ detects a distinction invisible to the ordinary $η$ invariant. The calculation uses spin-Fourier residues directly; perturbative Hessian signs serve only as motivation and are not part of the invariant.

Let $\mathcal{A}$ be a (not necessarily rational) conformal net with a faithful action of a finite group $G$. Let $\text{Rep}^G(\mathcal{A})$ be the $G$-crossed balanced $\mathrm{W}^*$-tensor category of $G$-twisted representations of $\mathcal{A}$ as introduced in arXiv:2606.03623. We show that there is an equivalence of balanced $\mathrm{W}^*$-tensor categories $(\text{Rep}^G(\mathcal{A}))^G\cong \text{Rep}(\mathcal{A}^G)$ between the $G$-equivariantization of $\text{Rep}^G(\mathcal{A})$ and the category of representations of the fixed-points conformal net $\mathcal{A}^G$. This generalizes to the non-rational case the equivalence of braided tensor categories $(\text{Rep}^G(\mathcal{A}))^G\cong \text{Rep}(\mathcal{A}^G)$ for $\mathcal{A}$ rational appearing (in the language of localized endomorphisms) in arXiv:math/0403322, and it also includes the balances.

Classical chance-constrained programs are solved by safe approximations based on the empirical CVaR, which uses a uniform measure over scenarios and systematically underweights tail events under heavy-tailed distributions. We introduce \emph{q-CCP}, a non-extensive safe approximation grounded in the Riemannian geometry of the Tsallis statistical manifold: the rank-based q-CVaR escort weights are the $g^{(q)}$-geodesic projection onto the tail simplex face, and the q-CCP feasible set is a Tsallis-divergence ball (Proposition~12). This geometric foundation yields three results. First, q-CCP is a provable strict tightening of CVaR-CCP for all $q > 1$ (Theorem~7). Second, the empirical violation ratio satisfies $ρ(q) = [1-(1-\varepsilon)^{q+1}]/\varepsilon$, independent of the tail index $ν$ (Proposition~10). Third, the feasible-region volume cost is monotone increasing in $q$ and $ν$ (Proposition~11), providing a data-adaptive safety knob. The formulation inherits convexity and coherence from the q-CVaR functional and admits an iterative LP reformulation converging in 2--3 iterations. Experiments on 15 Ibovespa equities confirm the theory (violation ratio $0.241$, $q^* = 1.50$); an M5 inventory newsvendor experiment generalises the method to supply chain ($q^* = 1.88$, cost premium $1.155\times$, zero OOS stockout violations).

The extension of the analytic fractal curve trees of (2601.17490} to analytic surface patch trees reveals a new geometric structure: branch points are replaced by interface curves that transmit the full analytical state of parent patches to their children. These interfaces prove to be central in determining the topology of the surface patch trees, including for the conditions for self-similarity of the interfaces, the patches and thus the trees. We establish the analytic conditions for the integrability and well-posedness of the surface patch trees and introduce further restrictions for conformality. We demonstrate that patch trees have a natural foliation that slices the trees into one dimensional curve trees, each of which has their own Hausdorff dimension, jointly creating a smooth dimension field. We extend the two dimensional surface model to arbitrary dimensions $n$ where $n-1$ interface manifolds transport the $n$ field state of the parent patches to their child branches. We note that the balance or discrepancy between patch field dimension and the dimensions in which the branches may evolve, determine the analytical regime from essentially geometrical to essentially operational.

We construct a periodic weighted graph whose discrete Laplacian has a spectrum with precisely $n$ gaps. Moreover, we show that by an appropriate choice of the weights, the endpoints of these gaps, as well as the upper edge of the spectrum, attain the prescribed values. The underlying graph has a brush-like geometry: it consists of an infinite chain of vertices, each of which is connected to $n$ additional pendant vertices by extra edges. Semi-explicit formulae for the weight coefficients are provided: some of the coefficients are determined explicitly, while others are given as roots of an explicitly determined polynomial.

We propose a phenomenological mass estimator for an intermediate ultralight axion dark-matter component using thin stellar streams. The central observation is an analytic relation linking three length scales in a fuzzy-dark-matter stream progenitor: the tidal radius of a bound dark core, its gravitational Bohr radius, and the axion de Broglie wavelength evaluated at the stripped-star velocity scale. If the stream width is (w=C_w r_{\rm t}), with (C_w=O(1)), then [ \frac{r_{\rm t}}{r_{\rm B}} =========================== \frac{4π^2}{C_w^2} \left(\frac{w}{λ_{\rm dB}}\right)^2 . ] Thus (λ_{\rm dB}\sim w) automatically implies (r_{\rm t}/r_{\rm B}\sim25)--(40): the dark wave core survives well inside the tidal boundary while the extended stellar envelope is stripped into a thin stream. This wave--tide locking gives a no-simulation axion-mass estimator, [ m_a \simeq 2.69\times10^{-19},{\rm eV} \left(\frac{\sqrt{2}}{q_κ}\right) \left(\frac{R}{10,{\rm kpc}}\right) \left(\frac{38,{\rm pc}}{w}\right)^2 \left(\frac{w}{\ell_{\rm ripple}}\right) \left(\frac{220,{\rm km,s^{-1}}}{v_c}\right). ] In the simplest locked case (\ell_{\rm ripple}\sim w), a homogeneous first-pass set of narrow stream widths points to (m_a) of a few (10^{-19},{\rm eV}) and hidden-core masses of a few (10^3)--(10^4M_\odot). This is not a detection claim; it is a falsifiable phenomenological test for an ultralight axion component that can be sharpened by homogeneous stream catalogs and Schrödinger--Poisson simulations.

We study the robustness of asymptotic entanglement manipulation beyond the exact i.i.d. regime, focusing on Mazzola--Sutter--Renner (MSR) almost i.i.d. sources, which allow a sublinear number of deviations from a tensor-power structure. For pure MSR sources along a bipartite reference state $|ϕ\rangle_{AB}$, we prove that the entanglement concentration rate is robust: every rate below the entropy of entanglement $S(ϕ_A)$ remains achievable. Moreover, this can be done by a single Schur--Weyl concentration protocol that is universal within the MSR class, depending only on the reference state and not on the particular source sequence. For mixed MSR sources along a reference state $ρ_{AB}$, we prove a source-dependent entanglement-distillation achievability result: every rate below the coherent information $I(A\rangle B)_ρ$ of the reference state is achievable, although the entanglement distillation protocol may depend on the particular MSR source sequence. For the reverse task of entanglement dilution, we prove a rate-robustness theorem: the asymptotic entanglement cost of any MSR target sequence along $ρ_{AB}$ is at most $E_F^\infty(ρ_{AB})$, the regularized entanglement of formation of the reference state. To establish these results, we prove structural and entropic properties of MSR almost i.i.d. sequences which may be useful in other information-theoretic settings. Thus, for the achievability statements considered here, MSR almost i.i.d. perturbations exhibit the same asymptotic behaviour as their i.i.d. reference states, despite allowing sublinear deviations from a tensor-power structure.

We report a photocurrent studies of a magic angle twisted bilayer graphene device using near infrared light. Through photocurrent imaging and polarization dependence, we separate the photo-thermoelectric effect from the photogalvanic effect. We observe a circular photogalvanic effect (CPGE) over a wide range of doping and temperature. The CPGE at normal incidence constraints the symmetry of the system to C$_1$, and points to a Berry curvature dipole, in agreement with theoretical predictions for strained graphene. Remarkably, the CPGE vanishes for filling $-2.5 < ν< -1.5$, suggesting an additional symmetry breaking in that regime. Insight into this effect is obtained through Berry curvature dipole calculations, which emphasize a novel symmetry breaking effect near $ν=-2$.

WebMCP is a newly emerging protocol that enables websites to expose tools directly to AI agents, bypassing traditional user interfaces and introducing new security risks. The dynamic exposure of agent-accessible tools in WebMCP expands the attack surface of web sessions, especially when third-party scripts are involved. In this study, we identify a new potential threat, termed Mid-Session Tool Injection (MSTI), in which attackers leverage third-party scripts to inject malicious tools during an active session. To better characterize this threat, we classify MSTI based on the stage and target of manipulation, distinguishing between Tool Hijacking and Tool Framing. Tool Hijacking modifies the set of tools visible to the agent through mechanisms such as the AbortSignal API or race conditions during tool registration. In contrast, Tool Framing influences the agent's perception of tool roles through metadata fields such as tool name, description, readOnlyHint, and inputSchema. Our implementation demonstrates that both Tool Hijacking and Tool Framing can successfully disrupt the intended functionality of WebMCP. Based on these results, we outline potential mitigation directions and provide security design recommendations for WebMCP, including binding tool identity to its origin, ensuring lifecycle consistency, enforcing data boundaries for third-party tools, and maintaining traceable logs of tool registration and invocation. These findings indicate that MSTI arises from WebMCP's unique tool lifecycle and structured metadata, making the tool surface itself an emerging security concern.

This paper presents the issues arising in implementing a fast integer division algorithm on general purpose GPUs. The algorithm uses a Newton iteration based on the shifted inverse operation, keeping all arithmetic in the integer domain and relying on data-parallel operators. The principal contribution is an efficient GPU/CUDA implementation for integer precisions from $2^{15}$ to $2^{18}$ -- sizes not supported by \cgbn{} division. We propose algorithmic refinements, define a cost model in terms of multiplications, build on prefix sums and previous work on multi-precision multiplication, and present an evaluation showing near-optimal performance relative to the model for the target precision.

The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $ξ^2_* = \sup_{λ\in \mathbb{R}} L(λ)$ where $L(λ) = \frac{2}{λ^2} \log \mathbb{E} e^{λX}$ is a weighted cumulant generating function. Despite the ubiquity of sub-Gaussian random variables, the estimation of $ξ^2_*$ has received little attention and is not yet well understood. In this work, we study a natural estimator of $ξ^2_*$ based on constrained maximization of the empirical analogue of $L$. We prove that the estimator is consistent bound the rates of convergence under assumptions on $L$: if $L$ has an maximizer, then our bound is $O_p(n^{-1/2 + \varepsilon})$ for any $\varepsilon > 0$; if the argmax of $L$ is also bounded, then the bound improves to $O_p(n^{-1/2})$. We show that our assumptions on $L$ are necessary by proving that the minimax risk over all sub-Gaussian distributions is $Ω(1)$; imposing increasingly strong assumptions on the tail growth of $L$ yields a continuum of classes whose minimax lower bound interpolates between $Ω(1/\log n)$ and $Ω(1)$. Root-n rate is possible if we restrict to a subclass of distributions where $L$ attains its supremum in a bounded region, in which case our estimator is minimax optimal. If the underlying distribution is not sub-Gaussian, we show that our estimator goes to infinity with a divergence rate controlled by the tail of the distribution. Finally, we apply our estimator in a Gene Ontology (GO) enrichment study to construct p-values for a large-scale permutation test, showing that it can serve as a reliable alternative to the peaks-over-threshold approach, particularly in regimes where the peaks-over-threshold method is of uncertain validity.

This work examines the effects of multiple parton radiation on proton-proton $W^\pm$ boson production at the Relativistic Heavy Ion Collider (RHIC), focusing on the ratio of charged lepton pseudorapidity differential cross sections to test the SU(2) flavor symmetry violation in the proton quark sea. I show that the measured ratio is minimally affected by the fiducial constraints imposed on the QCD recoil radiation by the STAR experiment, and that the ratio is also stable with respect to transverse momentum resummation effects. Hence, the STAR data on the $W^+/W^-$ cross section ratio provides a robust discrimination of $\bar{d}(x)$ and $\bar{u}(x)$ parton distribution functions (PDFs) at momentum fractions of order 0.1, shown by comparing predictions with various PDF models and using the $L_2$ sensitivity analysis and reweighting methods.

In the noncommutative polydisc, we first prove a positive sum of squares formula for a non-negative hereditary rational nc-function. The number of summands is finite. This result is used to derive a finite-dimensional realization formula for contractive nc-rational functions, where the colligation matrix is contractive. It is unitary if and only if the function is inner. Finally, we apply these results to generalize Carathéodory's classical theorem - approximating holomorphic self-maps of the unit disc by finite Blaschke products - to the setting of holomorphic functions on the noncommutative polydisc. This is in sharp contrast with the commutative situation where Carathéodory's approximation is known for Schur classes only in the unit disc and the unit bidisc.

We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion. The process converges to a unique opinion that, in expectation, is the degree-weighted average of the initial opinions. We show that if the graph has conductance $Φ(G)$, the ratio of the average to smallest degree is $γ(G)$, and the maximal difference between initial opinions is $K$, then the expected convergence time is ${O}\left({n\left(K\log (Kn)+γ(G) n \right)}/{Φ(G)^2}\right)$. This bound is essentially optimal for a large class of graphs of bounded expansion. We also show that for regular graphs, if the second largest eigenvalue is $o(1/\log^2 n)$ and $K$ is $o\left({n}/{\log^2 n}\right)$, then w.h.p.\ DIV converges to the initial average opinion (rounded up or down).

Whether cold dense QCD matter undergoes a strong first-order phase transition remains an open question. In nature, neutron stars provide the most direct probe of cold dense QCD matter. Theoretically, chiral effective field theory constrains the equation of state of dense matter near nuclear saturation density, while perturbative QCD calculations constrain it at densities well beyond stable neutron-star interiors. We perform Bayesian inference with non-parametric Gaussian-process equation of state for $β$-equilibrated neutron-star matter under the assumption with and without a strong first-order phase transition, using the tidal deformability from GW170817, the NICER mass--radius measurements of PSR~J0740$+$6620, PSR~J0030$+$0451, PSR~J0437$-$4715, PSR~J0614$-$3329, chiral effective field theory, and perturbative QCD. Our results favor a strong first-order phase transition, with its onset most likely lying \emph{above} the central density of the most massive neutron star. Such an onset reconciles the stiffness required to support massive neutron stars with the softening favored by perturbative QCD from asymptotically high density.