Testing Lorentz symmetry in strong gravitational fields provides a promising probe of extensions to general relativity. The supermassive black hole Sgr~A* and the orbit of the S-stars offer a laboratory for such tests in a regime beyond weak field limit. We analyze the S2 orbital data focusing on the Schwarzschild-like black hole within bumblebee gravity, where deviations from general relativity are encoded in a single Lorentz-violating parameter $\ell$. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain $\ell = {-8.01 \times 10^{-5}}^{+2.77 \times 10^{-4}}_{-2.09 \times 10^{-4}} $ and $\ell = {1.00 \times 10^{-5}}^{+2.90 \times 10^{-4}}_{-2.91 \times 10^{-4}} $ at $1σ$ confidence level, respectively. These constraints are about three orders of magnitude tighter than those from Event Horizon Telescope imaging of Sgr~A*.

Antiferromagnets have attracted significant attention because of their considerable potential in engineering high-density and ultrafast memory devices, a crucial and increasingly demanded component of contemporary high-performance information technology. Theoretical and experimental investigations are actively progressing to provide the capability of efficient switching and precise control of the Néel vector, which is crucial for the intended practical applications of antiferromagnets. Recently, a time-dependent Schwinger boson mean-field theory has been successfully developed to study the sublattice magnetization switching in anisotropic quantum antiferromagnets [K. Bolsmann $et \, al.$, \textcolor{blue}{\hyperlink{10.1103/PRXQuantum.4.030332}{PRX Quantum $\mathbf{4}$, 030332 (2023)}}]. Here we use a complementary exact diagonalization method to study such sublattice magnetization switching, but in small-cluster quantum antiferromagnets, by means of an external magnetic field. Furthermore, this article aims to support the findings of the Schwinger boson approach. We show that the results of both approaches are consistent at short time scales, with only about 12.5 $\%$ deviations. The consistency of the outcomes obtained through this alternative exact approach demonstrates that the time-dependent Schwinger boson mean-field theory is a versatile framework to capture the essentials of the switching process in quantum antiferromagnets. Thereby, the findings of current article pave the way for further theoretical and computational progress in the study of antiferromagnets for engineering spintronic devices with ultrahigh density and ultrafast speed.

In this work, we explore the $P$-wave resonance contributions to the three-body charmonium decays of $B_c\to Ψ(V\to) P_1P_2$ using the perturbative QCD formalism at leading order, where $Ψ$ denotes a $S$-wave charmonium state, such as $η_c(1S,2S),J/ψ$, and $ψ(2S)$. Here, $P_1P_2$ represents a collinear $ππ$ ($Kπ$) pair in the final state, which was primarily produced through the vector resonance $ρ(770)$ ($K^*(892)$ ). With the improved two-meson distribution amplitudes determined from our previous works, we examined the $CP$-averaged branching ratios and polarization fractions of the considered three-body decays. The longitudinal polarization fractions of the $B_c\to [J/ψ, ψ(2S)] (V\to) P_1P_2$ decays are found to be as large as $\sim 90\%$, since the transverse amplitudes from the dominant factorizable emission diagrams are always power suppressed with respect to the longitudinal ones. The direct $CP$ violations in $B_c\to Ψ(V\to) P_1P_2$ decays are predicted naturally to be zero as they solely receive contributions from tree diagrams. Several interesting relative ratios among the branching fractions of the concerned processes are investigated. In particular, the obtained ratio $R^{\rm PQCD}_{2π/π}\equiv \mathcal{B}(B^+_c \to J/ψ(ρ\to)π^+π^0)/{\mathcal{B}(B^+_c \to J/ψπ^+)}=2.67^{+0.21}_{-0.14}$ is consistent well with the LHCb measurement $R^{\rm exp}_{2π/π}=2.80\pm0.25$. Other similar ratios proposed in this work can be tested by LHCb experiments in the near future.

We construct a family of simple, lacunary hyperbolic groups with property $(T)$ that have rational cohomological dimension~$16$ and whose second $\ell^2$-Betti number can be prescribed to be any positive real. Moreover, we construct hyperbolic groups with property $(T)$ whose second $\ell^2$-Betti number can be prescribed to be any non-negative rational. Along the way, we present new constructions of measurably diverse finitely generated groups, and we prove that the second $\ell^2$-Betti number is far from being semi-continuous in the space of marked groups, even assuming good finiteness properties.

This paper presents a comprehensive review of community-centric power system resilience, emphasizing the integration of community-level resilience considerations and techno-legal governance frameworks with engineering-based resilience enhancement strategies and data-driven approaches to address extreme events. Recent large-scale outages have demonstrated that power disruptions can cascade beyond electrical infrastructure and disproportionately affect vulnerable communities, critical services, and interconnected urban systems, highlighting the need for resilience approaches that integrate technical, social, and regulatory dimensions. Within this community-centric perspective, the review first summarizes state-of-the-art strategies for enhancing power system resilience, including network hardening, resource allocation, optimal scheduling, and system reconfiguration techniques, while highlighting the growing role of artificial intelligence (AI) and data-driven analytics in supporting resilience planning and operational decision-making. It then examines the interdependencies between power system resilience and community resilience, addressing socioeconomic and behavioral dimensions, cross-infrastructure interconnections, and the emerging role of resilience hubs. The paper further examines the techno-legal frameworks governing resilient energy systems by comparing the regulatory landscapes of the European Union (EU) and the United States, highlighting key similarities and distinctions that shape resilience planning and implementation. By analyzing state-of-the-art engineering-based, AI-driven, and techno-legal methods for assessing and mitigating the impacts of high-impact, low-probability (HILP) events, the review identifies critical research gaps and outlines promising directions for future investigation.

Smart home automation that adapts to a user's emotional state can enhance psychological safety in daily living environments. This study proposes an emotion-aware automation framework guided by the emotional Biologically Inspired Cognitive Architecture (eBICA), which integrates appraisal, somatic responses, and behavior selection. We conducted a proof-of-concept experiment in a pseudo-smart-home environment, where participants were exposed to an anxiety-inducing event followed by a comfort-inducing automation. State anxiety (STAI-S) was measured throughout the task sequence. The results showed a significant reduction in STAI-S immediately after introducing the avoidance automation, demonstrating that emotion-based control can effectively promote psychological safety. Furthermore, an analysis of individual characteristics suggested that personality and anxiety-related traits modulate the degree of relief, indicating the potential for personalized emotion-adaptive automation. Overall, this study provides empirical evidence that eBICA-based emotional control can function effectively in smart home environments and offers a foundation for next-generation affective home automation systems.

We show that, on a standard non-atomic probability space, invertible measure-preserving transformations form a dense $G_δ$ subset of the space of all measure-preserving transformations endowed with the strong (=weak) operator topology. This implies that all properties which are generic for invertible transformations are also generic for general ones. We further show that invertible Koopman operators form a dense $G_δ$ subset of all bi-stochastic operators for the weak operator topology, and the same holds for general Koopman operators.

The nature of coherent radio emission is still challenging even after more than half a century of pulsar discovery, but it is generally a consensus that single-pulse observations are essential for probing the magnetospheric dynamics, especially with the largest single-dish telescope FAST (Five-hundred-meter Aperture Spherical radio Telescope). This paper aims to explain the observed diversity of single pulse circular polarization, and to constrain the multiplicity and Lorentz factor of pulsar magnetospheric plasma, with the mode coupling model in the limiting polarization region. Assuming that circular polarization comes only from wave mode coupling, we apply a Bayesian analysis to the FAST observed single pulse circular polarization spectra, involving numerical solving of wave mode coupling equations, and analyze the posterior probability distribution functions of the parameters. Although the model fails to quantitatively fit most circular polarization spectra, circular polarization of different frequency evolution is reproduced. For three chosen pulsars, the Bayesian analysis constrains the multiplicity to be approximately $10^{0}\sim10^{2}$, and the Lorentz factor to be approximately $10^{0.5}\sim10^{2}$. Pulsar circular polarization could be induced by wave mode coupling. The plasma flow responsible for coherent radio emission carries only a very small fraction of the pulsar spin-down energy loss.

We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point Padé expansion, to interpolate the weak and strong coupling expansions of correlation function. We benchmark this many-body interpolation approach on two prototypical models: the lattice $ϕ^4$ field theory and the 2D Hubbard model. For the $ϕ^4$ theory, the resulting two point Padé approximants exhibit uniform and global convergence to the exact correlation function. For the Hubbard model, we show that even at second order, the Padé appproximant already provides reasonable characterization of the Matsubara Green's function for a wide range of parameters. Finally, we offer a heuristic explanation for these convergence properties based on analytic function theory.

Let $G$ be a graph and $Γ$ a finite abelian group. The zero-sum Ramsey number of $G$ over $Γ$, denoted by $R(G, Γ)$, is the smallest positive integer $t$ (if it exists) such that any edge-colouring $c:E(K_t)\toΓ$ contains a copy of $G$ with $\sum_{e\in E(G)}c(e)=0_Γ$. We prove a linear upper bound $R(G, Γ)\leq Cn$ that holds for every $n$-vertex graph $G$ with bounded maximum degree and every finite abelian group $Γ$ with $|Γ|$ dividing $e(G)$.

We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of any large systems of algebraic equations). In space, we use Fourier Galerkin methods, while in time we use a combination of orthogonal projection and relaxation. We prove and numerically demonstrate the conservation properties of the method by applying it to the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger (NLS) PDEs as well as a hyperbolic approximation of NLS. For each of these equations, the proposed schemes conserve mass, momentum, and energy up to numerical precision. We show that this conservation leads to reduced growth of numerical errors for long-term simulations.

Robustness and adaptivity are two competing objectives in Kalman filters (KF). Robustness involves temporarily inflating prior estimates of noise covariances, while adaptivity updates prior beliefs by exploiting measurements. In practical applications, both process and measurement noise can be influenced by outliers, be time-varying, or both. In this work, we propose a variational robust Kalman filter, built on a Student's $t$-distribution induced loss function and variational inference, and solved in a computationally efficient manner. We demonstrate that robustness can be understood as a prerequisite for adaptivity, making it possible to merge the above two competing goals into a single framework through a probabilistic switching rule. Additionally, our proposed filter can recover conventional KF, robust KF, and adaptive KF by tuning parameters, and can suppress both the imperfect process and measurement noise, enabling it to perform superiorly in complex noise environments. Simulations verify the effectiveness of the proposed method.

We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and Fisher-Shannon complexity track the effective frequency $ω_{\mathrm{eff}}=ω\sqrt{1-κ}$ of the potential. We show that the Fisher information and Shannon entropy reflect an effective frequency-driven redistribution of information between conjugate spaces. Our results show that the Fisher-Shannon complexity measure remains invariant under effective frequency control. The invariance demonstrates that optical modulation of $κ$ rescales localization, without altering the harmonic structure of the motional states. These results establish a controlled information-theoretic baseline for lattice-assisted Paul traps. Beyond the harmonic limit, retaining the quartic lattice correction introduces non-Gaussian wavefunction features through state-dependent mixing of higher eigenstates, which breaks the mutual compensation between Fisher information and Shannon entropy that sustains the invariant. The departure of $P'$ from its harmonic reference value intensifies with $κ$ and is stronger for the excited state, which confirms that the Fisher-Shannon complexity invariance is a distinctive property of the small-oscillation harmonic regime.

Concerns about AI-generated political content are growing, yet there is limited empirical evidence on how deepfakes actually appear and circulate across social platforms during major events in democratic countries. In this study, we present one of the first in-depth analyses of how these realistic synthetic media shape the political landscape online, focusing specifically on the 2025 Canadian federal election. By analyzing 187,778 posts from X, Bluesky, and Reddit with a high-accuracy detection framework trained on a diverse set of modern generative models, we find that 5.86% of election-related images were deepfakes. Right-leaning accounts shared them more frequently, with 8.66% of their posted images flagged compared to 4.42% for left-leaning users, often with defamatory or conspiratorial intent. Yet, most detected deepfakes were benign or non-political, and harmful ones drew little attention, accounting for only 0.12% of all views on X. Overall, deepfakes were present in the election conversation, but their reach was modest, and realistic fabricated images, although less common, drew higher engagement, highlighting growing concerns about their potential misuse.

A numerical semigroup $S$ is a cofinite subsemigroup of $ \mathbb{N}$, where $\mathbb{N}$ is the additive monoid of non-negative integers. Denote by $\mathcal{P}_{\rm fin} (S)$ the semigroup consisting of all non-empty finite subsets of $S$ endowed with the operation of setwise addition defined by $$X+Y=\{x+y:x\in X, y\in Y\}, \qquad\text{for all } X, Y \in \mathcal P_\text{fin}(S).$$ We call $\mathcal{P}_{\rm fin} (S)$ the finitary power semigroup of $S$. When $0\in S$ (and hence $S$ is a numerical monoid), the family $\mathcal P_{\text{fin},0}(S)$ of all finite subsets of $S$ containing $0$ is a submonoind of $\mathcal P_\text{fin}(S)$; we call $\mathcal{P}_{{\rm fin}, 0}(S)$ the reduced finitary power monoid of $S$ with the singleton $\{0\}$ as zero-element. For a non-empty finite subset $X$ of $\mathbb{N}$, we denote by $ \min X$ and $\max X $ the minimum and the maximum in $X$. Tringali and Yan have recently proved in [J.\ Combin.\ Theory Ser.\ A 209 (2025)] that the only non-trivial automorphism of $\mathcal{P}_{{\rm fin},0}(\mathbb{N})$ is the involution $X \mapsto \max X - X$. By applying Tringali-Yan's result, we in this article determined the automorphism group of the finitary power semigroup $\mathcal{P}_{\rm fin}(S)$ of an arbitrary numerical semigroup $S$. More precisely, if $S$ is the set of all integers larger than or equal to a fixed $k \in \mathbb N$, then the only non-trivial automorphism of $\mathcal{P}_{\rm fin}(S)$ is the involution $X \mapsto \max X - X+ \min X$; otherwise, $\mathcal{P}_{\rm fin}(S)$ has only the identity automorphism.

In the exascale computing era, handling and analyzing massive datasets have become extremely challenging. In situ analysis, which processes data during simulation runtime and bypasses costly intermediate disk input and output steps, offers a promising solution. We present libyt (https://github.com/yt-project/libyt), an open-source C library that enables astrophysical simulations to analyze and visualize data in parallel computation with yt or other Python packages. libyt can invoke Python routines automatically or provide interactive entry points via a Python prompt or a Jupyter Notebook. It requires minimal intervention in researchers' workflow, allowing users to reuse job submission scripts and Python routines. We describe libyt's architecture for parallel computing in high-performance computing environments, including its bidirectional connection between simulation codes and Python, and its integration into the Jupyter ecosystem. We detail its methods for reading patch-based adaptive mesh refinement (AMR) simulations and handling in-memory data with minimal overhead, and procedures for yielding data when requested by Python. We describe how libyt maps simulation data to yt frontends, allowing post-processing scripts to be converted into in situ analysis with just two lines of change. We document libyt's API and demonstrate its integration into two astrophysical simulation codes, GAMER and Enzo, using examples including core-collapse supernovae, isolated dwarf galaxies, fuzzy dark matter, the Sod shock tube test, Kelvin-Helmholtz instability, and the AGORA galaxy simulation. Finally, we discuss libyt's performance, limitations related to data redistribution, extensibility, architecture, and comparisons with traditional post-processing approaches.

In recent years, compact nanodosimetric detectors based on ion multiplication in low-pressure gas have been developed and gained attention in the scientific community. These detectors use strong electric fields to collect and multiply positive ions produced by the incident radiation in mm-sized cell holes in dielectric materials, achieving a nm-equivalent spatial resolution of the localization of ionization events, when scaled to liquid water at unit density. Their design assumes that ion-impact ionizations of gas molecules within the cell holes dominate signal formation, yet this assumption has lacked direct physical verification. Electron emission from the cell hole walls or the cathode due to ion-impact could also contribute, requiring alternative designs to optimize efficiency. To investigate the relative importance of the possible mechanisms, a nanodosimetric detector featuring a single cell hole with a diameter of 1.5 mm in a dielectric plate was developed. Ion collection and multiplication were achieved by applying a negative high voltage to the glass cathode 0.5 mm below the cell hole, assisted by a low drift field above the plate. A grounded readout electrode with a 0.8 mm hole covers the cell hole to prevent interactions of collected ions with the hole walls. High signal yields in 1 mbar and 2 mbar propane gas were observed and indicated that ion-impact ionizations of the gas molecules could indeed be the primary mechanism for signal induction. Ion-induced secondary electron emission from the cathode was identified as another potential contribution. The compact nanodosimeter setup was further modeled with Geant4-DNA and Garfield++ for deeper insight. The results of these studies are important for understanding and developing a new class of nanodosimeters with potential applications in particle therapy, radiation protection, space dosimetry, and particle physics.

Deep learning potentials for complex many-body systems often face challenges of insufficient accuracy and a lack of physical realism. This paper proposes an "Observable-Constrained Variational Framework" (OCVF), a general top-down correction paradigm designed to infuse physical realism into theoretical "skeleton" models (H_o) by imposing constraints from macroscopic experimental observables (\mathfrak{O}_{\text{exp},s}). We theoretically derive OCVF as a numerically tractable extension of the "Constrained-Ensemble Variational Method" (CEVM), wherein a neural network (ΔH_θ) learns the correction functional required to match the experimental data. We apply OCVF to BaTiO3 (BTO) to validate the framework: a neural network potential trained on DFT data serves as H_o, and experimental PDF data at various temperatures are used as constraints (\mathfrak{O}{\text{exp},s}). The final model, H_o + ΔH_θ, successfully predicts the complete phase transition sequence accurately (s', s \neq s'). Compared to the prior model, the accuracy of the Cubic-Tetragonal (C-T) phase transition temperature is improved by 95.8\% , and the Orthorhombic-Rhombohedral (O-R) T_c accuracy is improved by 36.1\%. Furthermore, the lattice structure accuracy in the Rhombohedral (R) phase is improved by 55.6\%, validating the efficacy of the OCVF framework in calibrating theoretical models via observational constraints.

In classical factorization theory, an integral domain is called \emph{atomic} if every nonzero nonunit element can be written as a finite product of irreducible elements. Here, we introduce and study a weaker notion of atomicity, which relaxes the requirement that all elements admit a factorization into irreducibles. Namely, we say that an integral domain is \emph{sub-atomic} if every nonunit divisor of an atomic element is also atomic. We further consider several factorization properties associated with this notion. Then, we investigate the basic properties of such domains, provide examples, and explore the behavior of the sub-atomic property under standard constructions such as localization, polynomial rings, and $D+M$ constructions. Our results highlight the independence of the sub-atomic property from other classical factorization properties and introduce an important class of integral domains that lies between atomic and non-atomic domains.

Loi-Piergallini, Akbulut-Ozbagci, and Akbulut-Arikan showed that every compact Stein surface admits a positive allowable Lefschetz fibration over the disk $D^2$ with bounded fibers (PALF in short), and they provided constructions of PALF's corresponding to compact Stein surfaces. In this paper, we present a simple method for constructing a PALF from a 2-handlebody decomposition of any given compact Stein surface. Our method yields PALF's whose regular fibers have small genus, and it provides an alternative constructive proof of the above result. We also define the minimal genus of a regular fiber of a PALF on the knot trace of a knot $K$ with framing one less than its maximal Thurston-Bennequin number as an invariant of $K$. When the grid number of $K$ is $N$, our construction produces a PALF whose regular fiber has genus at most $(N - 1)/2$, showing that the defined invariant is bounded above by $(N - 1)/2$.

An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by second-order stochastic partial differential equations (SPDE). In particular, an infinite-dimensional linear state-space representation is obtained where the state transition is governed by a proposed SDE. Then, using the Galerkin's method, a finite-dimensional approximation to the infinite-dimensional SDE is obtained, yielding a dynamical model with finite states that facilitates computation and parameter estimation. The space-time covariance of the approximated dynamical model is obtained, and the error between the approximate and exact covariance matrices is quantified. Comprehensive numerical investigations, including 2D wave equation, seismic wave propagation, advection-diffusion equations and wildfire aerosol propagation processes, are performed to demonstrate the application of the proposed model. Code is available.

Let $q=p^f$ be a prime power, $H \leq \mathrm{GL}_d(q)$ a subgroup containing a genuine Singer cycle $s$ of order $q^d-1$, and $W$ an $\mathbb{F}_q H$-module whose scalar extension restricts to an untwisted polynomial tensor representation $\bigotimes L(λ^{(t)})$ of the algebraic group $\mathrm{GL}_d$. If the total polynomial degree satisfies $K < q-1$, we prove that distinct weights give distinct eigenvalues of $s$ on $W \otimes_{\mathbb{F}_q} \mathbb{F}_{q^d}$. The proof relies on an elementary base-$q$ injectivity lemma: bounded digit vectors determine distinct residues modulo $q^d-1$. Consequently, when the tensor product is multiplicity-free for the diagonal torus, the Singer cycle has a simple spectrum. We also provide a shifted exponent formula for situations where Singer eigenvalue data undergo $q$-Frobenius shifts, proving separation of distinct shifted digit vectors under the same bound $K<q-1$. These results provide a uniform spectral explanation for eigenvalue separation in bounded-degree polynomial tensor representations. Motivated by this, we formulate a conditional rewriting framework that uses compatible base-$q$ eigenvalue labelling to reduce the reconstruction of the natural action to a functor-specific inversion problem. Finally, the viability of this framework is explicitly demonstrated through computational experiments, prominently featuring a non-trivial, full algebraic reconstruction of the natural action from a strictly multiplicity-free, genuine tensor product representation.

Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this issue for logistic regression, but their relative performance under realistic conditions remains poorly understood. We therefore conducted a preregistered, simulation-based comparison of 28 established methods for variable selection and inference under model uncertainty, using 11 empirical datasets spanning a range of sample sizes and number of predictors, in cases both with and without separation. We found that Bayesian model averaging (BMA) methods based on g-priors, particularly g = max(n, p^2), show the strongest overall performance when separation is absent. When separation occurs, penalized likelihood approaches, especially the LASSO, provide the most stable results, while BMA with the local empirical Bayes (EB-local) prior is competitive in both situations. These findings offer practical guidance for applied researchers on how to effectively address model uncertainty in logistic regression in modern empirical and machine learning research.

We develop a novel holographic framework to study dynamical phases in random quantum circuits with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a non-symmetric layer, composed of random multiplicity tensors. For $G\,{=}\,\mathbb{Z}_N$ symmetric circuits consisting of local unitary gates interspersed with local symmetric noise channels, averaging over the non-symmetric layer yields a dynamically generated noisy $\mathbb{Z}_{N}$ surface code. This allows us to interpret $\mathbb{Z}_{N}$ symmetric circuits in the volume-law phase as quantum error-correcting codes with a distinguished set of logical spin states that inherit the topological protection of the bulk code. By establishing equality of bulk and boundary coherent information, we show that quantum information encoded in these logical states is maximally protected against symmetric noise up to a finite threshold. We further study weakly monitored $\mathbb{Z}_{N}$ symmetric circuits which exhibit a charge-sharpening transition. We show that the point at which the observer gains classical information about the global charge coincides with the point at which measurements destroy the underlying quantum information encoded in the bulk surface code. This also allows for a natural interpretation of the sharpening transition as a confinement transition in the gauge theory. For $N\,{\leq}\,4$, weak measurements drive a single transition from a charge-fuzzy phase with exponential sharpening time $t_{\#}\sim e^{L}$ to a charge-sharp phase with $t_{\#}\sim \mathcal{O}(1)$. On the other hand, for $N>4$, the circuit can enter an intermediate phase with a linear sharpening time $t_{\#}\sim \mathcal{O}(L)$. In this regime, the bulk gauge theory realizes a Coulomb phase with emergent gapless photons.

Sweat evaporation is the body's primary cooling mechanism, yet the physical factors governing it are not fully understood. We identify a dueling buoyancy effect in the context of the human body, in which perspiration vapor reduces the near skin air density, counteracting the downward flow driven by cooling of warm air upon contact with the skin. In hot, arid, stagnant environments, this opposing buoyancy suppresses free convection and can reduce sweat evaporation by more than half. As a result, commonly used thermoregulation models can substantially underpredict body temperature (e.g., by 1C after 2 hours of exposure to typical Arizona summer conditions). We develop compact, physics informed models for free convective heat transfer coefficients across wide temperature and humidity ranges, enabling improved thermoregulation modeling and thermal audits. These results enhance understanding of human heat balance and support more accurate heat stress assessment to inform behavioral, infrastructural, and policy decisions for extreme heat adaptations.

Serving deep learning based recommendation models (DLRM) at scale is challenging. Existing approaches rely on dedicated ANN indexing and filtering services on CPUs, suffering from non-negligible costs and missing co-design opportunities. Such inefficiency makes them difficult to support complex model architectures, such as learned similarities and multi-task retrieval. In this paper, we present SilverTorch, a model-based serving system that brings all components into one unified model. It unifies model serving by replacing standalone indexing and filtering services with model layers. We propose a model-based GPU Bloom index for feature filtering and a fused Int8 ANN kernel for nearest neighbor search. Through co-design of the ANN search and feature filtering, we reduce GPU memory usage and eliminate computation. Benefiting from this design, we scale up retrieval by introducing an OverArch scoring layer and a multi-task retrieval with a Value Model to aggregate scores. These advancements improve the retrieval accuracy and enable future studies for serving more complex models. Our evaluation on industry-scale datasets show that SilverTorch achieves up to 23.7\times higher throughput compared to the state-of-the-art approaches. We also demonstrate that SilverTorch solution is 13.35\times more cost-efficient than CPU-based solution while improving accuracy via serving more complex models. SilverTorch is deployed at scale, serving hundreds of models online and supporting recommendation for diverse applications.

In-context learning (ICL) allows LLMs to adapt to new tasks via a few demonstrations, but those demonstrations may contain sensitive data. Differentially private (DP) ICL mechanisms mitigate this risk by injecting noise into the aggregation step, but verifying that an implementation actually meets its claimed privacy bound currently requires repeated end-to-end membership-inference attacks (MIAs) against the pipeline as a black box, incurring prohibitive LLM cost and yielding unstable empirical privacy estimates. We propose SnapAudit, an active auditing framework that decomposes a DP-ICL pipeline into a deterministic clean-inference stage and a stochastic DP-noise stage, and audits the full pipeline by combining a small snapshot of the former with bootstrap simulation of the latter. Because clean LLM outputs are near-deterministic at temperature zero, a few thousand clean LLM calls suffice to approximate the snapshot distribution; SnapAudit then bootstraps $10^5$ noisy trials from this snapshot at negligible additional cost, with finite-sample uncertainty controlled via an empirical Bernstein correction. For embedding-based mechanisms, we further introduce a multi-sweep search procedure that constructs maximally separable audit signals. SnapAudit achieves $80$--$200\times$ speedup over prior passive auditing while producing tighter and more stable empirical privacy estimates that closely match theoretical guarantees. Beyond efficiency, SnapAudit uncovers two concrete flaws in existing DP-ICL designs: (i) classical Gaussian noise calibrations underestimate leakage at large privacy budgets, allowing empirical leakage to exceed the theoretical bound; (ii) the sensitivity analysis of an embedding-aggregation mechanism is incorrect when the number of partitions equals one, leading to undersized noise and an outright privacy violation.

Existing auction mechanisms are vulnerable to bidder collusion, which substantially degrades revenue and non-colluder welfare. To design truthful mechanisms resilient to collusion, we introduce a novel approach that leverages a machine learning classifier to predict (even imprecisely) which bidders are colluding. We first establish a Bulow-Klemperer-type result for multi-unit auctions with single-minded bidders, demonstrating that collusion significantly harms existing mechanisms only when the colluding coalition is large. Consequently, we focus our design on settings with many colluders. Building on the welfare-optimal Vickrey-Clarke-Groves (VCG) mechanism, we propose two novel truthful mechanisms: VCG-Posted Price (V-PoP) and Conditional-Posted Price (C-PoP). V-PoP applies VCG to non-colluding bidders and posted prices to colluding ones, and ensuring truthfulness is non-trivial because we must dynamically split the quantity of items between these groups based on the values of the non-colluder bids. C-PoP further advances this by computing a posted price conditioned on non-colluder bids, and ensuring truthfulness is non-obvious because the posted price is chosen using the values of the non-colluder bids. Because real-world classifiers make errors, we provide theoretical lower bounds on the auction price of V-PoP and C-PoP under misclassification, which theory shows acts as a proxy for welfare and revenue. Crucially, our bounds yield actionable insights for classifier design, revealing that false negatives (misclassifying colluders as non-colluders) are preferable to false positives (misclassifying non-colluders as colluders). Numerical experiments demonstrate that our mechanisms achieve high welfare and revenue against collusion, even when utilizing simple, low-cost classifiers.

Instrumental variables (eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We propose an IV estimator that synthesizes instruments from the data. We establish finite-sample $L^{p}$ consistency for all $p \ge 1$ in both discrete- and continuous-time models, recovering a nonparametric $\sqrt{n}$-convergence rate. On a forced Lorenz system our estimator reduces parameter bias by 200x (continuous-time) and 500x (discrete-time) relative to least squares and reduces RMSE by up to tenfold. Because the method only assumes that the model is linear in the unknown parameters, it is broadly applicable to modern sparsity-promoting dynamics learning models.

Consider the action of a subgroup $G$ of the permutation group on the polynomial ring $S := k[x_{1}, \ldots, x_{n}]$ via permutations. We show that if $k$ does not have characteristic two, then the following are independent of $k$: the $a$-invariant of $S^{G}$, the property of $S^{G}$ being quasi-Gorenstein, and the Hilbert functions of $H_{\mathfrak{m}}^{n}(S)^{G}$ as well as $H_{\mathfrak{n}}^{n}(S^{G})$; moreover, these Hilbert functions coincide. In particular, being independent of characteristic, they may be computed using characteristic zero techniques, such as Molien's formula. In characteristic two, we show that the ring of invariants is always quasi-Gorenstein, compute the $a$-invariant explicitly, and show that the Hilbert functions of $H_{\mathfrak{m}}^{n}(S)^{G}$ and $H_{\mathfrak{n}}^{n}(S^{G})$ agree up to a shift, given by the number of transpositions. We determine when the inclusion $S^{G} \hookrightarrow S$ splits, thereby proving the Shank--Wehlau conjecture for permutation subgroups. Lastly, we determine the ring of $k$-linear differential operators on $S^{G}$, and show that each differential operator lifts to one over $\mathbb{Z}$.