Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.

In this work, we propose a novel experimental set-up using charged resonant gravitational wave detectors. We exploit the semi-classical analogue of the Gertsenshtein effect where the gravitational wave acts as an modulator for the optomechanical system. We consider a cavity QED scenario where the Weber bar is placed inside an electromagnetically shielded cavity. We observer that when the gravitational wave falls on the Weber bar, it emits photon which signifies the detection of gravitational waves by the resonant bars. The frequency controlled spontaneous emission scenario will shed a new light on future generation of efficient gravitational wave detector models.

A countable discrete group $Γ$ is said to have the relative ISR-property if for every non-trivial normal subgroup $N\trianglelefteqΓ$ and every von Neumann subalgebra $\mathcal{M}\subseteq L(Γ)$ invariant under conjugation by $N$, one has $\mathcal{M}=L(K)$ for some subgroup $K\leΓ$. Similarly, $Γ$ has the relative $C^*$-ISR-property if every $N$-invariant unital $C^*$-subalgebra $\mathcal{A} \subseteq C_r^*(Γ)$ is of the form $C_r^*(K)$. We show that every torsion-free acylindrically hyperbolic group with trivial amenable radical satisfies the relative ISR property. Moreover, we also show that all torsion-free hyperbolic groups have the relative $C^*$-ISR property. Furthermore, we establish an analogous relative ISR-property for irreducible lattices in higher-rank semisimple Lie groups, such as $\mathrm{SL}_d(\mathbb{Z})$ ($d \geq 3$), with trivial center.

Tidal disruption events (TDEs) can be observed when stars get too close to supermassive black holes and are torn apart and accreted. The delay time distribution of TDEs, or rate of TDEs as a function of time since a burst of star formation, can be used to determine what mechanisms influence the TDE rate. We compile a catalog of 41 TDE host galaxies with optical spectra, model the stellar populations with Bagpipes, and retrieve the age of the most recent burst of star formation to construct the delay time distribution of TDEs. TDEs occur more frequently in post-starburst galaxies than in other types of galaxies, though the mechanism causing this rate enhancement is unknown. We find that the TDE rate increases with post-burst age to reach a peak at ~1 Gyr relative to a control sample. We compare the observational TDE delay time distribution to theoretical models, which propose overdense stellar nuclei, radial anisotropies in stellar orbits, supermassive black hole binaries, and AGN disks as potential mechanisms that may enhance the TDE rate in post-starburst galaxies. Most models predict a TDE rate that declines with post-burst age, in contrast to our observational results, though some models are still feasible at certain ages (e.g., the black hole binary model matches at old burst ages and the stellar overdensity model matches at intermediate burst ages).

Using the hydrodynamical (fluid) approximation, we present a self-consistent theoretical framework that couples the origin, evolution and decay of spiral structures to the secular dynamical evolution of their host galactic disks. Our approach highlights non-resonant spiral excitation through azimuthal forcing that leverages mild, pervasive gradients in the disk's mass and angular momentum distributions, structural features we term cavernae. These cavernae are weaker but more widespread than the sharp features behind groove mode excitation and commonplace in exponential disks. We discuss how non-resonant features combine with other responses -- resonant dressing, steady waves, groove modes -- to produce a global, evolving spiral nexum that transports angular momentum and reshapes the disk. Using expressions for torques, angular momentum transport and heating, we demonstrate that global spirals are intrinsically self-limiting; the angular momentum changes and heating they generate quenches their own growth, dictating a finite lifetime for any single spiral episode. A succession of transient episodes, each with properties adjusted to the changed disk conditions, lays the pathway to long-lived spiral activity. This behavior suggests that the character of secular evolution shifts over time. We find that the short-lived, high-multiplicity (high-m) spirals that dominate in dynamically cold disks induce widespread, impulse-like non-resonant heating, yet with a low ratio of heating to radial migration. As the disk warms, high-m features are suppressed, leading to steadier, lower-m spirals that heat progressively more efficiently near resonances. In this light, the dynamical coldness of disk galaxies today requires a past dominated by high-m transient perturbations, whereas warmer, more compact systems reflect an advanced stage of evolution regulated by transient, low-m spirals.

We study the spectral gaps of parallel and simulated tempering chains targeting multimodal Gibbs measures. In particular, we consider chains constructed from Metropolis random walks that preserve the Gibbs distributions at a sequence of harmonically spaced temperatures. We prove that their spectral gaps admit polynomial lower bounds of order $11$ and $12$ in terms of the low target temperature. The analysis applies to a broad class of potentials, beyond mixture models, without requiring explicit structural information on the energy landscape. The main idea is to decompose the state space and construct a Lyapunov function based on a suitably perturbed potential, which allows us to establish lower bounds on the local spectral gaps.

Data-driven reachability analysis enables safety verification when first-principles models are unavailable. This requires constructing sets of system models consistent with measured trajectories and noise assumptions. Existing approaches rely on zonotopic or box-based approximations, which do not fit the geometry of common noise distributions such as Gaussian disturbances and can lead to significant conservatism, especially in high-dimensional settings. This paper builds on ellipsotope-based representations to introduce mixed-norm uncertainty sets for data-driven reachability. The highest-density region defines the exact minimum-volume noise confidence set, while Constrained Convex Generators (CCG) and their matrix counterpart (CMCG) provide compatible geometric representations at the noise and parameter level. We show that the resulting CMCG coincides with the maximum-likelihood confidence ellipsoid for Gaussian disturbances, while remaining strictly tighter than constrained matrix zonotopes for mixed bounded-Gaussian noise. For non-convex noise distributions such as Gaussian mixtures, a minimum-volume enclosing ellipsoid provides a tractable convex surrogate. We further prove containment of the CMCG times CCG product and bound the conservatism of the Gaussian-Gaussian interaction. Numerical examples demonstrate substantially tighter reachable sets compared to box-based approximations of Gaussian disturbances. These results enable less conservative safety verification and improve the accuracy of uncertainty-aware control design.

We obtain boundary nondegeneracy and regularity estimates for solutions to non-divergence form parabolic equations in parabolic $C^1$ domains, providing explicit moduli of continuity. Our results extend the classical Hopf-Oleinik lemma and boundary Lipschitz regularity for domains with $C^{1,\mathrm{Dini}}$ boundaries, while also recovering the known $C^{1-\varepsilon}$ regularity for parabolic Lipschitz domains, unifying both regimes with a single proof.

In higher-dimensional Einstein-AdS gravity, it is well known that planar and static anti-de Sitter black holes can be endowed with multiple rotation parameters via a large-gauge transformation. However, a similar prescription fails when multiple NUT parameters are added, thereby obstructing the study of holographic properties with more than one NUT charge. To pave the way towards this direction, we construct explicit planar AdS spacetimes having multiple NUT parameters in two simple ways that allow one to circumvent the strong restrictions imposed by the vacuum field equations. First, motivated by momentum relaxation holographic models, we construct multi-NUT spaces in AdS with flat horizons by adding free scalar fields possessing an axionic profile. In our second approach, we build similar configurations in Einstein gravity with quadratic-curvature corrections. As a byproduct, we end by presenting planar versions of the Kaluza-Klein monopole in AdS with different magnetic charges.

Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH--KCBS scenario involving the entanglment of a qubit and a qutrit, the qutrit supports the KCBS contextuality test, and the CHSH nonlocality arises from correlations between the qubit and qutrit. Here, we derive the analytical closed-form expressions for both inequalities and also simulate this physics on a quantum circuit. We show that contextuality is governed solely by a population parameter $p_2$, associated with the occupation of the qutrit subsystem in the $|2\rangle$ level, which plays a distinguished role in the KCBS structure. In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$. This separation of physical resources reveals parameter regimes that optimize KCBS violation while suppress CHSH violation, and vice versa. As a result, the optimal regions do not overlap, and coexistence is restricted to a narrow intermediate regime in parameter space.

Galactic cosmic rays (CRs) are a fundamental non-thermal component of the interstellar medium (ISM). Understanding the transport of super-high-energy particles is essential for interpreting observations of Galactic PeVatrons. Classical diffusion models assuming a homogeneous and isothermal medium oversimplify the multiphase ISM. We utilize high-resolution 3D MHD simulations to self-consistently generate a multiphase ISM, comprising the warm (WNM), unstable (UNM), and cold neutral medium (CNM), and investigate 1.5-15 PeV particle transport using a test-particle approach. We find that thermal phase transitions induce steep magnetic field strength gradients at phase boundaries, creating localized magnetic fluctuations that act as efficient sites for adiabatic mirror reflections and non-adiabatic pitch-angle scattering, strongly enhancing cross-field transport at these interfaces. However, because phase boundaries occupy only a small volume fraction and particles spend most of their trajectory in the weakly scattering WNM and UNM, the global pitch-angle scattering coefficient in the multiphase ISM is smaller than in an equivalent isothermal medium. This locally strong scattering nevertheless drives both parallel and perpendicular spatial diffusion coefficients to $\sim10^{30} {\rm cm^2 s^{-1}$ at 1.5~PeV, with the perpendicular component exceeding its isothermal counterpart ($\sim 10^{28}{\rm cm^2 s^{-1}$) by two orders of magnitude. Using a phase--phase diffusion matrix decomposition, we show that global CR transport is governed by the volume-filling, trans-Alfvénic WNM and UNM, where particles stream along stochastically wandering field lines. Cross-phase displacement correlations are universally positive, indicating cooperative transport between thermal phases. In contrast, the super-Alfvénic CNM acts as an efficient confinement that substantially suppresses local diffusion.

Ping Xu generalized Drinfeld 2-cocycles from bialgebras to associative bialgebroids over noncommutative base algebras. Any counital Drinfeld--Xu 2-cocycle twists the base algebra of the bialgebroid and a comultiplication on the total algebra, obtaining a new, twisted bialgebroid. Antipodes for bialgebroids have been considered, but finding a general way to twist the antipode, which is straightforward in the Hopf algebra case, appeared somewhat elusive. In this article, we prove that if an invertible antipode $S$ for the original bialgebroid exists, and another expression $V_F$ depending on the 2-cocycle $F$ is invertible, then the expected conjugation formula $S_F(-) = V_F^{-1} S(-) V_F$ indeed produces an invertible antipode $S_F$ for the twisted bialgebroid.

Large language models (LLMs) are increasingly used as quantitative research copilots to translate natural-language strategy specifications into executable trading code. Yet most existing evaluations either focus on static financial knowledge or summarize performance with a single profitability metric, leaving a gap for benchmarking strategy-to-code trading systems as governed, auditable software. We introduce SysTradeBench (SysTB), an iterative build-test-patch benchmark that evaluates LLM-generated trading systems under drift-aware diagnostics. Given a standardized Base Strategy Doc and frozen semantics, each model must produce (i) a strategy card, (ii) executable code, and (iii) mandatory audit logs. A sandboxed harness runs determinism and anti-leakage checks, detects rule drift across iterations, and returns evidence bundles to support constrained patches. SysTradeBench reports multi-dimensional scorecards for spec fidelity, risk discipline, reliability, and out-of-sample robustness indicators, together with cost-effectiveness signals. We evaluate 17 models across 12 strategies. Top models achieve validity above 91.7 percent with strong aggregate scores, but evidence-driven iteration also induces code convergence by Iter2. These findings suggest that LLM iteration complements rather than replaces human quantitative researcher governance: LLMs excel at rapid prototyping and shallow bug fixes, while human oversight remains essential for critical strategies requiring solution diversity and ensemble robustness.

We present an independent pipeline for detecting candidate vanished sources on digitized first-epoch Palomar Observatory Sky Survey (POSS-I) photographic plates. The pipeline detects and PSF-filters sources on POSS-I Red DSS cutouts, applies local astrometric registration refinement, and identifies candidates by cross-epoch matching against POSS-I Blue and POSS-II Red with Pan-STARRS DR1 rejection. On a 20-case benchmark harness, the pipeline recovers 8/9 sources in the April 1950 field and 3/3 in the July 1952 field, with a false positive rate of about 0.2 per 10 arcmin field on random non-crowded controls. A full-footprint sweep over the POSS-I coverage using 30 arcmin patches yields a filtered catalog of 2.85 million candidate vanished sources after post-processing PSF cuts, deduplication, and Pan-STARRS DR1 rejection. Cross-matching against the published 5,399-source Solano et al. (2022) catalog yields 3,450 matches (63.9%) with median separation 0.94 arcsec; among unrecovered catalog entries within our footprint, we find no Pan-STARRS DR1 counterpart within 3 arcsec. Applying Bruehl and Villarroel (2025)-style temporal windows to this catalog over the 368 POSS-I observation nights in the 1949-1957 interval gives a post-test calendar-day relative risk of 1.35 for the +1 day window, but the effect is not statistically significant (95% CI 0.91-2.00; two-sided Fisher p = 0.17) and is sensitive to coding unobserved days as zero-transient days. A negative binomial model of nightly candidate counts with nightly patch coverage as exposure is likewise null (IRR = 1.03, 95% CI 0.89-1.18, p = 0.71). The catalog-level replication is strong; the temporal association remains inconclusive.

As software proliferates across domains, its aggregate energy footprint has become a major concern. To reduce software's growing environmental footprint, developers need to identify and refactor energy smells: source code implementations, design choices, or programming practices that lead to inefficient use of computing resources. Existing catalogs of such smells are either domain-specific, limited to performance anti-patterns, lack fine-grained root cause classification, or remain unvalidated against measured energy data. In this paper, we present a comprehensive, language-agnostic, taxonomy of software energy smells. Through a systematic literature review of 60 papers and exhaustive snowballing, we coded 320 inefficiency patterns into 12 primary energy smells and 65 root causes mapped to the primary smells. To empirically validate this taxonomy, we profile over 21,000 functionally equivalent Python code pairs for energy, time, and memory, and classified the top 3000 pairs by energy difference using a multi-step LLM pipeline, mapping 55 of the 65 root causes to real code. The analysis reveals that 71% of samples exhibit multiple co-occurring smells, memory-related smells yield the highest per-fix energy savings, while power draw variation across patterns confirms that energy optimization cannot be reduced to performance optimization alone. Along with the taxonomy, we release the labeled dataset, including energy profiles and reasoning traces, to the community. Together, they provide a shared vocabulary, actionable refactoring guidelines, and an empirical foundation for energy smell detection, energy-efficient code generation, and green software engineering at large.

We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized principal-components estimator of Song and Zou (2026), which enjoys a blessing-of-dimensionality phenomenon under predictor contamination but senstive for heavy-tailed data or outliers. We replace the squared loss by a Wilcoxon-type rank loss and then apply a one-step adaptive reweighting scheme to reduce the shrinkage bias of the initial $\ell_1$ fit. The resulting procedure combines robustness to heavy-tailed response errors with the contamination geometry induced by the empirical principal-components basis. Our main theorem gives a prediction bound for the fixed-$λ$ second-stage fitted mean. Simulations show that the rank-based procedure is competitive under Gaussian noise and substantially more stable under heavy-tailed errors, especially when predictor contamination is present.

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang--Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar $0^{++}$ glueball is found to be exceptionally compact, with a radius of order the instanton size, $ρ\sim \frac 13\,\mathrm{fm}$, consistent with lattice indications. By contrast, the tensor $2^{++}$ state remains spatially extended due to the centrifugal barrier. We also discuss the role of $S$-$D$ mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.

This Research Note is in response to the recent paper by S. M. Perriyil et al. (2026). They provide measurements of the time delay (delta t) between the hard X-ray and soft X-ray peak times for 96 flares observed with RHESSI and GOES. These delays are found to be dependent on the length of 9 the magnetic loop(s) joining the HXR footpoints seen in RHESSI images. We offer a possible explanation for this coincidence in terms of the duration of the electron beam heating, commonly inferred from the duration of the HXR emission, and the time taken for heated plasma to rise to the loop top as inferred in this paper from delta t. We suggest that the particle acceleration occurs at or near the top of the loop(s) and that it is quenched by the increase in density as the heated plasma reaches the acceleration site.

Residue Number Systems (RNS) offer efficient modular arithmetic and natural parallelism, but direct integer division in RNS remains a difficult and comparatively underdeveloped operation. This paper builds on the type-II division algorithm of Szabo and Tanaka and reformulates it for more efficient hardware implementation. A principal contribution is the introduction of a power-based RNS, in which moduli are selected as powers of natural primes, increasing dynamic range, improving bit efficiency, and providing greater flexibility for scaling during division. The paper further formalizes three decomposition methods required by the division process: multi-factor scaling for modulus-based division, mixed-radix conversion for base extension and comparison, and a new divisor decomposition method introduced in this work. Each method is supported by mathematical development, including analysis of modulus invalidation during computation. These results simplify the hardware structure of the algorithm and improve its scalability. Supported by hardware diagrams and performance tables, the work advances both the theory and practical implementation of direct RNS division.

We present an elementary state augmentation method for a class of static risk measure applied to the total cost for both Markov decision processes and stochastic optimal control, such that dynamic programming equations can be derived on the augmented space. Through this we discuss the sample complexities of these two problems for both finite-horizon and infinite-horizon settings. We demonstrate the application of the proposed approach through studying distributionally robust functional generated by $ϕ$-divergences including conditional value-at-risk.

Using DESI SV3 spectroscopic group centrals together with deep HSC photometric data, we measure the conditional luminosity functions (CLFs) of central and satellite galaxies, separately for red and blue populations, in dark matter halos spanning $M_h\sim10^{12}- 10^{15}M_{\odot}$ and $0<z<1$. The depth of the HSC imaging enables CLFs to be measured to unprecedentedly faint limits, reaching $M_r \approx -15$ at $0.2 \leqslant z < 0.5$ and $M_r \approx -17$ at $0.5 \leqslant z < 1.0$. We find a remarkably weak evolution in the CLF of satellite galaxies over $0<z<1$. The Blue satellite CLFs are well described by a single Schechter function across all halo masses and redshifts, with a nearly constant slope of $-1.25\lesssim α\lesssim -1.2$. In contrast, red satellite CLFs exhibit a pronounced and ubiquitous faint-end upturn in all halo mass and redshift bins, with little evolution in the faint-end slope ($-1.8\lesssim α_f\lesssim -1.7$). These results indicate that the low-mass end of the red sequence in clusters/groups was already established by $z\sim1$. Both satellite characteristic magnitudes and central galaxy luminosities fade with time. Red central galaxies are consistent with passive evolution, whereas the luminosity evolution of blue centrals is dominated by ongoing star formation. Satellite galaxies evolve more rapidly than predicted by simple stellar population models, highlighting the importance of environmental effects. The quenched fraction of satellite galaxies as a function of stellar mass exhibits a universal minimum at $M_{\ast} \sim 10^9M_{\odot}$, independent of halo mass and redshift. We discuss possible interpretations of these results and their implications for galaxy formation and evolution.

We provide an infinite series of commutative finite-dimensional Gorenstein local algebras $A_n$ for $n \ge 2$. We give an elementary proof that the maximal ideal of every algebra $A_n$ possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of $A_n$. The latter implies that the algebras $A_n$ fail the affine homogeneity property. We also discuss some consequences concerning additive actions on projective hypersurfaces, related to the generalized Hassett-Tschinkel correspondence for these algebras.

The unscented Kalman filter (UKF) is a commonly used algorithm capable of estimating the states of nonlinear dynamic systems. It carefully chooses a set of sample points, called sigma points that capture the nonlinear system states posterior mean and covariance. The filter is based on the scaled unscented transform, where the scaling parameters impact the spreading of the sigma points, determining the estimated model capturing. In its current form, the UKF employs a single set of scaling parameters shared by all sigma points. Because states in multi-dimensional models often exhibit substantially different behaviors, this imposes a critical limitation: the standard UKF parameters cannot be tuned to extend the spread for one dimension while reducing it for another. To bridge this gap, we propose the multi-scaled UKF to enable spreading differently per state, while maintaining the key properties of the sigma points and UKF. A rigorous mathematical foundation is provided, introducing a novel theoretical approach to multi-scaling. The benefits of this approach are demonstrated through two distinct nonlinear dynamic systems. Consequently, our multi-scaled UKF captures the nonlinear behavior of multi-dimensional states more effectively, leading to improved estimation accuracy.

PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.

Large language models (LLMs) produce systematically misleading outputs, from hallucinated citations to strategic deception of evaluators, yet these phenomena are studied by separate communities with incompatible terminology. We propose a unified taxonomy organized along three complementary dimensions: degree of goal-directedness (behavioral to strategic deception), object of deception, and mechanism (fabrication, omission, or pragmatic distortion). Applying this taxonomy to 50 existing benchmarks reveals that every benchmark tests fabrication while pragmatic distortion, attribution, and capability self-knowledge remain critically under-covered, and strategic deception benchmarks are nascent. We offer concrete recommendations for developers and regulators, including a minimal reporting template for positioning future work within our framework.

We study bootstrap inference for the $k$th largest coordinate of a normalized sum of independent high-dimensional random vectors. Existing second-order theory for maxima does not directly extend to order statistics, because the event $\{T_{n,[k]}\le t\}$ is not a rectangle and its local structure is governed by exceedance counts rather than by a single boundary. We develop an approach based on factorial moments and weighted inclusion--exclusion that reduces the problem to a collection of rare-orthant probabilities and allows high-dimensional Edgeworth and Cornish--Fisher expansions to be transferred to the order-statistic setting. Under moment, variance, and weak-dependence conditions, we derive a second-order coverage expansion for wild-bootstrap critical values of the $k$th order statistic. In particular, a third-moment matching wild bootstrap achieves coverage error of order $n^{-1}$ up to logarithmic factors, and the same second-order accuracy is obtained for a prepivoted double wild bootstrap. We also show that the maximal-correlation condition can be replaced by a stationary Gaussian exponential-mixing assumption at the price of an explicit dependence remainder $r_d$, and this remainder can itself be of order $n^{-1}$ when the dimension is sufficiently large relative to the sample size. These results extend recent second-order Gaussian and bootstrap approximation theory from maxima to the $k$th order statistic in high dimension.

We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $θ$ variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $γ_{ij}$. These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for scalar field dark matter models and stochastic quantum gravity.

Deploying large language models (LLMs) as cloud services raises privacy concerns as inference may leak sensitive data. Fully Homomorphic Encryption (FHE) allows computation on encrypted data, but current FHE methods struggle with efficient and precise nonlinear function evaluation. Specifically, CKKS-based approaches require high-degree polynomial approximations, which are costly when target precision increases. Alternatively, TFHE's Programmable Bootstrapping (PBS) outperforms CKKS by offering exact lookup-table evaluation. But it lacks high-precision implementations of LLM nonlinear layers and underutilizes GPU resources. We propose \emph{TIGER}, the first GPU-accelerated framework for high-precision TFHE-based nonlinear LLM layer evaluation. TIGER offers: (1) GPU-optimized WoP-PBS method combined with numerical algorithms to surpass native lookup-table precision limits on nonlinear functions; (2) high-precision and efficient implementations of key nonlinear layers, enabling practical encrypted inference; (3) batch-driven design exploiting inter-input parallelism to boost GPU efficiency. TIGER achieves 7.17$\times$, 16.68$\times$, and 17.05$\times$ speedups over a CPU baseline for GELU, Softmax, and LayerNorm, respectively.

Large language models are increasingly deployed as autonomous agents in multi-agent settings where they communicate intentions and take consequential actions with limited human oversight. A critical safety question is whether agents that publicly commit to actions break those promises when they can privately deviate, and what the consequences are for both themselves and the collective. We study deception as a deviation from a publicly announced action in one-shot normal-form games, classifying each deviation by its effect on individual payoff and collective welfare into four categories: win-win, selfish, altruistic, and sabotaging. By exhaustively enumerating announcement profiles across six canonical games, nine frontier models, and varying group sizes, we identify all opportunities for each deviation type and measure how often agents exploit them. Across all settings, agents deviate from promises in approximately 56.6% of scenarios, but the character of deception varies substantially across models even at similar overall rates. Most critically, for the majority of the models, promise-breaking occurs without verbalized awareness of the fact that they are breaking promises.