Managing patients with respiratory failure increasingly involves noninvasive respiratory support (NIRS) strategies to support respiration, often preventing the need for invasive mechanical ventilation. However, despite the rapidly expanding use of NIRS, there remains a significant challenge to its optimal use across all medical circumstances. It lacks a unified ontological structure, complicating guidance on NIRS modalities across healthcare systems. This study introduced NIRS ontology to support knowledge representation in acute care settings by providing a unified framework that enhances data clarity and interoperability, laying the groundwork for future clinical decision-making. We developed NIRS ontology using the Web Ontology Language (OWL) and Protege to organize clinical concepts and relationships. To enable rule-based clinical reasoning beyond hierarchical structures, we added Semantic Web Rule Language (SWRL) rules. We evaluated logical reasoning by adding a sample of 6 patient scenarios and used SPARQL queries to retrieve and test targeted inferences. The ontology has 145 classes, 11 object properties, and 18 data properties across 949 axioms that establish concept relationships. To standardize clinical concepts, we added 392 annotations, including descriptive definitions based on controlled vocabularies. SPARQL query evaluations across clinical scenarios confirmed the ontology ability to support rule based reasoning and therapy recommendations, providing a foundation for consistent documentation practices, integration into clinical data models, and advanced analysis of NIRS outcomes. In conclusion, we unified NIRS concepts into an ontological framework and demonstrated its applicability through the evaluation of patient scenarios and alignment with standardized vocabularies.

We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in applications ranging from control theory to modeling collective multi-agent behavior (e.g., bird flocks, traffic dynamics) under hierarchical leadership. The IM learning problem is formulated as solving nonlinear functional equations derived from the invariance equation, expressing the manifold as a relationship between exogenous and system states. The proposed approach combines polynomial series with shallow neural networks, leveraging their complementary strengths. We focus on low- to medium-dimensional manifolds where polynomial expansions remain tractable. Near equilibrium, polynomial series provide interpretability and convergence, while farther away neural networks capture global structure through their universal approximation capability. A continuity penalty enforces consistency between both representations at their interface, and training is performed using analytically derived derivatives within the Levenberg-Marquardt scheme. Naturally, depending on the dimensionality of the input-driven system, one may also employ a purely neural network-based IM approximation, for which we also establish a universal approximation theorem based on certain assumptions on system dynamics. The framework is evaluated on two benchmark problems: an enzymatic bioreactor and a leader-follower car-following model. We analyze convergence, approximation accuracy, and computational cost, and compare standalone neural networks, polynomial expansions, and the hybrid method. Results show that the hybrid approach achieves superior accuracy compared to standalone schemes.

We explore how minimal neural networks can invert the renormalization group (RG) coarse-graining procedure in the two-dimensional Ising model, effectively ``dreaming up'' microscopic configurations from coarse-grained states. This task - formally impossible at the level of configurations - can be approached probabilistically, allowing machine learning models to reconstruct scale-invariant distributions without relying on microscopic input. We demonstrate that even neural networks with as few as three trainable parameters can learn to generate critical configurations, reproducing the scaling behavior of observables such as magnetic susceptibility, heat capacity, and Binder ratios. A real-space renormalization group analysis of the generated configurations confirms that the models capture not only scale invariance but also reproduce nontrivial eigenvalues of the RG transformation. While the inversion is necessarily imperfect, these minimal models robustly reproduce the RG-relevant structure of the critical distribution. Surprisingly, we find that increasing network complexity by introducing multiple layers offers no significant benefit. These findings suggest that simple local rules, akin to those generating fractal structures, are sufficient to encode the universality of critical phenomena, creating an opportunity for efficient generative models of statistical ensembles in physics.

With the widespread adoption of vibe coding, understanding the reasoning and robustness of Large Language Models (LLMs) is critical for their reliable use in programming tasks. While recent studies assess LLMs' ability to predict program outputs, most focus on accuracy alone, without evaluating the underlying reasoning. Moreover, it has been observed on mathematical reasoning tasks that LLMs can arrive at correct answers through flawed logic, raising concerns about similar issues in code understanding. In this paper we assess whether state-of-the-art LLMs can reason about Python programs or are simply guessing. We apply five semantics-preserving code mutations: renaming variables, mirroring comparison expressions, swapping if-else branches, converting for loops to while, and loop unrolling. These mutations maintain program semantics while altering its syntax. We evaluated nine LLMs, including both open-source and closed-access models, and performed a human expert analysis using LiveCodeBench to assess whether correct predictions are based on sound reasoning. We also evaluated prediction stability across different code mutations on LiveCodeBench and CruxEval. While proprietary models achieve the strongest predictive accuracy and reasoning quality in the expert evaluation, our robustness analysis reveals substantial fragility under semantics-preserving transformations. Our findings show that LLMs trained for code produce correct predictions based on flawed reasoning in between 10% and 50% of cases. Furthermore, LLMs often change predictions in response to our code mutations, with performance drops reaching up to 70%, indicating that they do not yet exhibit stable, semantically grounded reasoning, even when initial accuracy is high.

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.

We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with stochastic gradient descent. This includes high-dimensional linear regression, kernel regression, and linear random feature models. Our results include previously known asymptotics as well as novel ones.

We introduce a foundation model for event classification in high-energy physics, built on a Graph Neural Network architecture and trained on 120 million simulated proton-proton collision events spanning 12 distinct physics processes. The model is pretrained to learn a general and robust representation of collision data using challenging multiclass and multilabel classification tasks. Its performance is evaluated across seven event classification tasks, which include new physics processes not encountered during pretraining as well as ATLAS Open Data to demonstrate generalizability across different simulation frameworks, from Delphes fast simulation to full ATLAS detector simulation. Fine-tuning the pretrained model significantly improves classification performance, particularly in scenarios with limited training data, demonstrating gains in both accuracy and computational efficiency. To investigate the underlying mechanisms behind these performance improvements, we employ a representational similarity evaluation framework based on Centered Kernel Alignment. This analysis reveals that encoder-stage representations of the fine-tuned model remain similar to those of the baseline, while intermediate graph processing layers diverge substantially, indicating that fine-tuning preserves general-purpose encoders while developing fundamentally different message-passing pathways to arrive at superior task performance.

In recent years, diffusion models have emerged as a superior alternative to generative adversarial networks (GANs) for high-fidelity image generation, with wide applications in text-to-image generation, image-to-image translation, and super-resolution. However, their real-time feasibility is hindered by slow training and inference speeds. This study addresses this challenge by proposing a wavelet-based conditional Diffusion GAN scheme for Single-Image Super-Resolution (SISR). Our approach utilizes the diffusion GAN paradigm to reduce the timesteps required by the reverse diffusion process and the Discrete Wavelet Transform (DWT) to achieve dimensionality reduction, decreasing training and inference times significantly. The results of an experimental validation on the CelebA-HQ dataset confirm the effectiveness of our proposed scheme. Our approach outperforms other state-of-the-art methodologies successfully ensuring high-fidelity output while overcoming inherent drawbacks associated with diffusion models in time-sensitive applications. The code is available at https://www.github.com/aloilor/WaDiGAN-SR

From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited to deep neural networks. This balance of phenomenological richness with analytical tractability makes ridge regression the model system of choice in high-dimensional machine learning. In this paper, we present a unifying perspective on recent results on ridge regression using the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning. We highlight the fact that statistical fluctuations in empirical covariance matrices can be absorbed into a renormalization of the ridge parameter. This `deterministic equivalence' allows us to obtain analytic formulas for the training and generalization errors in a few lines of algebra by leveraging the properties of the $S$-transform of free probability. From these precise asymptotics, we can easily identify sources of power-law scaling in model performance. In all models, the $S$-transform corresponds to the train-test generalization gap, and yields an analogue of the generalized-cross-validation estimator. Using these techniques, we derive fine-grained bias-variance decompositions for a very general class of random feature models with structured covariates. This allows us to discover a scaling regime for random feature models where the variance due to the features limits performance in the overparameterized setting. We also demonstrate how anisotropic weight structure in random feature models can limit performance and lead to nontrivial exponents for finite-width corrections in the overparameterized setting. Our results extend and provide a unifying perspective on earlier models of neural scaling laws.

Deploying pretrained visual models in real-world environments often suffers from significant performance degradation due to the diversity of testing scenarios. Continuous adaptation of learning models on edge devices via unlabeled data collected from the target domain is highly effective for boosting generalization capability. However, gradient-backpropagation-based optimization of the massive parameters in deep neural networks is vastly more time-consuming than forward inference, rendering online learning infeasible on low-power edge devices. To address this critical challenge, we propose a lightweight gradient-free forward-memorizing framework, namely MemFlow, which leverages a frozen backbone and enables efficient fine-tuning of the mapping between features and predictions. Specifically, MemFlow employs randomly connected neurons to memorize feature-label associations; within the network, spiking signals are propagated, and predictions are generated by associating neuron-stored memories according to their confidence levels. More notably, MemFlow supports reinforced memorization of feature mappings using unlabeled data, thereby enabling rapid adaptation to new domains. Extensive experiments on four real-world cross-domain datasets demonstrate that MemFlow achieves performance improvements of up to 10\% while consuming less than 1\% of the computational time required by traditional domain adaptation methods.The code is available at https://github.com/so-link/MemFlow.

In this paper, a $\mathbb{Q}$HD singularity is a weighted homogeneous normal surface singularity admitting a rational homology disk ($\mathbb{Q}$HD) smoothing. These singularities are rational but often not log canonical. We classify all $\mathbb{Q}$HD degenerations of nonsingular projective elliptic surfaces, extending Kawamata's classification of the case with only Wahl singularities (i.e., log terminal $\mathbb{Q}$HD singularities). We also realize all $\mathbb{Q}$HD degenerations of Dolgachev surfaces $D_{a,b}$ with one $\mathbb{Q}$HD singularity, for every pair of integers $a,b$. For each such degeneration, we construct a minimal semi log canonical (slc) birational model via a Seifert partial resolution in the sense of Wahl followed by semistable flips. Finally, we prove that these minimal slc models are unobstructed and deform to the recent degenerations of Dolgachev surfaces constructed by D. Lee and Y. Lee.

Quantum thermalization describes how interacting quantum systems relax toward thermal equilibrium, a central problem in modern physics. Yet most experimental information on many-body systems comes from short-time transition spectroscopy, typically interpreted within Kubo's linear-response framework. These perspectives - long-time equilibration versus short-time response - seem fundamentally disconnected. Here we establish an exact link between them: the Kubo-Thermalization correspondence, which connects long-time thermalized magnetization under weak driving to short-time linear-response spectra for a spin coupled to a thermal bath. The correspondence holds even when the steady state differs substantially from the initial state and when each regime is individually difficult to describe theoretically. We experimentally confirm the correspondence using effective spin-1/2 impurities realized with ultracold fermions in two internal states coupled to a Fermi sea. Our results provide a rare exact statement about quantum thermalization and offer a novel route to infer thermalization dynamics from equilibrium response measurements in strongly interacting quantum systems, independent of microscopic details of the system-bath coupling.

The radial acceleration relation (RAR) links observed and baryonic accelerations, and is best established in rotation curves of late-type galaxies. Pulsar timing, which measures line-of-sight (LOS) differential accelerations between the Sun and pulsars, provides a novel probe of this relation, including along directions outside the Galactic disc. By combining these pulsar differential accelerations with the acceleration at the Sun, we test whether current pulsar timing data carry information on a vector generalisation of the RAR, ${g}_{\rm obs}=ν(|{g}_{\rm bar}|){g}_{\rm bar}$. Comparing the measured SPARC RAR (generalised to 3D) to 26 binary-system pulsars with literature accelerations, we find a reduced $χ^2$ of 3.58, compared with 10.86 for Newtonian baryonic gravity alone. However, setting all accelerations to that of the Sun gives a reduced $χ^2$ of 3.75, showing that this vector RAR test is dominated by the Solar acceleration with current data.

Heat dissipation is critical in modern engineering systems. Polymer additives offer a potential route to improve fluid-based cooling. Here, we study elasticity-enhanced heat transfer in two-dimensional, thermally-stratified Poiseuille flow. At Reynolds numbers, $Re$, $\lesssim 1000$, we observe two types of linearly unstable modes: the recently identified elasticity-induced centre mode (Khalid et al., J. Fluid Mech. 915, 2021) and the classical buoyancy-driven convective mode (Kelly, Adv. Appl. Mech. 31, 35-112, 1994). Direct numerical simulations show that the centre mode develops into a nonlinear `arrowhead' state but yields negligible heat transfer enhancement (typically $\approx 0.03\%$ increase compared to the conductive state). By contrast, polymers can enhance the heat flux associated with the convective mode by up to $1100\%$. The nonlinear convective-mode states take the form of either periodic orbits or travelling waves, and are dominated by hook-like polymer-stress structures that can attach to the walls. The unattached hooks act as `speed bumps' that reduced streamwise velocity and promote wall-normal motion, whereas wall-attached hooks form effective `polymer walls', reorganising the flow into strong counter-rotating rolls and triggering the extreme-enhancement regime. The elasto-buoyant nature of these states is confirmed by perturbation kinetic energy budgets, which show that polymer and buoyancy sustain the states synergistically. The wall-attached hooks enable rapid thermal equilibration but impose a large hydraulic penalty, making them suitable for process streams requiring fast temperature adjustment. Unattached hooks provide a more thermally efficient regime for heat-transport applications. These results highlight the potential of elastic fluids for future heat transfer enhancement technologies.

Covariate adjustment is a general method for improving precision when estimating treatment effects in randomized trials and is recommended by the FDA in its 2023 guidance when baseline variables are prognostic for the primary outcome. We focus on a method highlighted in that guidance called ``standardization" (or ``g-computation") for estimating the marginal treatment effect. We address the question of how to reliably estimate variance for binary outcomes when marginal outcome probabilities are close to 0 or 1. We propose an influence function-based leave-one-out cross-validated (IF-LOO) variance estimator for the standardized difference-in-means average treatment effect. Through simulation studies, we show that this estimator provides appropriate type-I error control and performs reliably in challenging settings where existing methods can yield inflated type-I error or fail entirely, such as when outcome events are rare or sample sizes are small. In addition to having desirable statistical properties, we derive a closed-form expression for the proposed estimator, enabling straightforward and reliable implementation by study statisticians. The robust finite-sample performance and ease of implementation suggest the IF-LOO variance estimator is a prudent default choice for standardization in clinical trials.

We propose a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the other end of the SymTFT slab. Each such boundary condition gives an absolute completion of the same relative theory, so the ensemble is interpreted as an average over topological completions rather than over arbitrary local dynamics. We formulate this construction in terms of cap functionals and their natural groupoid or Haar-type measures, and illustrate it in two examples. In the closed-string sector of the Marolf--Maxfield model, topological boundary conditions are labelled by finite sets, and the groupoid sum reproduces the Poisson/Bell-polynomial moments. In the Narain case, compact topological boundary conditions of an $\mathbb{R}$-valued BF SymTFT are identified with maximal isotropic subgroups, so that topological-boundary averaging becomes the usual Narain moduli average with Zamolodchikov measure. We also discuss possible extensions to JT gravity, random matrix theory, Virasoro T(Q)FT, and 3D gravity.

The emergence of colossal magnetoresistance in a new generation of Eu$^{2+}$-based antiferromagnets is intriguing given stark contrasts to the archetypal perovskite manganites and doped Eu-chalcogenides. In this study the thermal conductivity and magnetostriction of Eu$_5$Sn$_2$As$_6$ -- one such representative -- have been measured to better understand the role of the crystal lattice. Both properties are strongly field-dependent and mirror the magnetization, saturating once the Eu$^{2+}$ moments are polarized. The field-enhancement of the phonon-dominated thermal conductivity is interpreted through the lifting of a degeneracy of spin configurations, and the subsequent saturation due to quenched magnetostrain in high field. Comparison with spin-glass insulators suggests that this phenomenon is not a byproduct but rather the driver of electron delocalization due to the suppression of strong phonon scattering arising from exchange frustration.

The ever-increasing demand for fast, reliable, and energy-efficient information storage continues to push magnetic memory technologies toward their fundamental limits. Conventional scaling strategies, which rely on reducing bit size, inevitably run into the "magnetic recording trilemma," where signal-to-noise ratio, thermal stability, and writability cannot all be optimized simultaneously. Heat-assisted magnetic recording (HAMR) has emerged as the leading solution, enabling high-density storage by transiently heating the medium during the write cycle. However, the reliance on laser optics and plasmonic transducers restricts HAMR primarily to hard-disk drives, limiting its integration with on-chip or embedded architectures. Here, we demonstrate an electronic variant of HAMR in which Joule heating from low-current density current pulses facilitates data writing, while the anomalous Hall effect provides electronic readout. Employing intercalated 2D magnet Ni$_{1/4}$TaSe$_2$, we show direct evidence that current pulses heat the material above its Curie temperature, during which a small magnetic field of ~2mT (100 times smaller than the coercive field) enables efficient data writing. The all-electronic approach combined with the 2D magnetic medium creates timely opportunities to revisit the energy-assisted magnetization recording, enabling new recording schemes that combine fundamental novelty with technological impact.

We describe libwignernj, a freely available, BSD-licensed library that evaluates Wigner 3j, 6j, and 9j symbols, Clebsch--Gordan, Racah $W$, and Fano $X$ coefficients, and Gaunt coefficients over both complex and real spherical harmonics in standards-compliant C99. libwignernj represents factorials by the vector of their signed prime-exponent decomposition - a prime-factorization technique introduced for the angular-momentum coefficients by Dodds and Wiechers (Comput. Phys. Commun. 4, 268 (1972)) and refined in a long line of subsequent work - and combines that representation with the multiword-integer Racah sum of Johansson and Forssén (SIAM J. Sci. Comput. 38, A376 (2016)), under which every intermediate quantity is an exact rational and all rounding is confined to the final floating-point conversion. Single-, double-, and long-double-precision results are correct to the last representable bit, and IEEE 754 binary128 evaluation through libquadmath and arbitrary-precision evaluation through the GNU Multiple-Precision Floating-Point Reliable (MPFR) library are optionally exposed. libwignernj has no mandatory runtime dependencies and no caller-side initialization step, making it easy to embed across the atomic, molecular, nuclear, and electromagnetic-scattering applications in which these coefficients arise. C++, CPython, and Fortran 90 bindings ship alongside the C library. Half-integer angular momenta are encoded exactly via integer $2j$ arguments throughout the application programming interface (API). CMake-package and pkg-config files ship for drop-in integration into downstream projects, and a continuous-integration (CI) pipeline runs the full test suite on Linux (shared and static), macOS, and Windows on every push.

Large audio language models (LALMs) are increasingly used to reason over long audio clips, yet deployment often compresses audio before inference to reduce memory and latency. The risk is that compression can leave aggregate accuracy acceptable while sharply degrading answers for a deployment-critical query family. We study answer-preserving audio compression, judging a compressor by the excess answer-error it induces, especially for the worst-affected family. We formulate this theoretically as a compressor acceptance-rejection criterion, derive a practical sign-off protocol that returns compression budgets satisfying worst-family checks with statistical confidence, and evaluate it on five multiple-choice audio question-answering benchmarks with two Qwen-based backbones. The protocol exposes hidden family-level damage, shows that the chosen query-family partition can change the approved budget, and identifies regimes where query-conditioned compression helps maintain answer preservation.

Safety-critical autonomy in adversarial settings demands more than Lyapunov stability of tracking error signals. An agent executing a goal-directed trajectory is intrinsically legible to a passive observer running online Bayesian inference, because the contractive dynamics of any Lyapunov basin of attraction concentrates posterior belief over the latent intent parameters. We initiates the study of intent privacy over a continuous state space as a joint control problem on the physical state combined with the latent belief state of a putative observer. With the main challenges concentrated around the analysis of the belief-state dynamics, the agent dynamics is assumed to be simple, modeled by the differential inclusion $\dot{x}\in u+\bar{d}\mathbb{B}$. That is, the agent is fully actuated with bounded unknown disturbance to the control input. The observer's intent inference process is modeled as a discrete-time stochastic dynamical system evolving over the belief state space of a Rao Blackwellized particle filter reasoning over large random samples of possible agent goals. The agent's control input is modeled as a piecewise constant signal, with jumps matching the RBPF update times. Building on a prior intent-inference framework and its KL-based information leakage measurement, a privacy constraint is imposed, which amounts to maintaining information leakage above a prescribed threshold with high probability, using probabilistic discrete-time control barrier functions. A key technical contribution is the derivation of separate PCBF results for the Bayesian update step and the resampling step of the RBPF, enabling a PCBF result for the full update as well as integration of the privacy constraint with the agent's task-side tracking requirement. Finally, a joint feasibility analysis is carried out by examining the interplay between the privacy constraint and the tracking envelope.

We consider a Hamiltonian system on the symplectic space $({\mathbb{R}}^{2n}, dy\wedge dx)$ with a real-analytic Hamiltonian $H : {\mathbb{R}}^{2n}\to {\mathbb{R}}$. We assume that the system has a non-degenerate equilibrium position at the origin. Under some nonresonance assumptions we prove the following. For any positive integer $M$ there exists a real-analytic function $F:{\mathbb{R}}^{2n}\to{\mathbb{R}}$ such that (1) $F = O\big( (|x|+|y|)^{M+1} \big)$ at the origin, (2) the system with Hamiltonian $H+F$ is completely integrable in ${\mathbb{R}}^{2n}$.

This paper demonstrates the expand-contract plasticity of the unit spheres of $\ell_1$, $\ell_{\infty}$, and $c$. Furthermore, it establishes the strong plasticity of the unit spheres of Hilbert spaces.

Let $d \in \mathbb{N}$, $δ\in (0, 1/2)$, and $X > 0$. Denote by $N_d(X, δ)$ the maximum number of points in a subset of the closed Euclidean ball of radius $X$ in $\mathbb{R}^d$ such that every pairwise distance is at least $δ$ away from any integer. In the planar case, Sárközy proved that for every $\varepsilon > 0$, $N_2(X, δ) = Ω_δ(X^{1/2-\varepsilon})$ as $X \rightarrow \infty$ whenever $δ$ is sufficiently small in terms of $\varepsilon$, while Konyagin proved the almost matching upper bound $N_2(X,δ) = O_δ(X^{1/2})$. We study this problem in higher dimensions, addressing a question of Erdős and Sárközy. Extending Sárközy's construction, we show that for every $\varepsilon > 0$, $N_3(X, δ) = Ω_δ(X^{1-\varepsilon})$ for $δ$ sufficiently small in terms of $\varepsilon$. We also provide a lifting lemma from integer distance sets to sets avoiding near-integer distances via bilipschitz embeddings of snowflaked Euclidean spaces. This allows us to prove a linear lower bound $N_4(X,δ) = Ω_δ(X)$ for all sufficiently small $δ$. Finally, adapting Konyagin's approach, we prove the upper bound $N_d(X, δ) = O_{d, δ}(X^{d/2})$ for all $d \in \mathbb{N}$.

Bayesian Optimization (BO) is a popular framework for optimizing black-box functions. Despite its effectiveness, BO is often inefficient for high-dimensional problems due to the exponential growth of the search space, heterogeneity of the objective function, and low sampling budget. To overcome these issues, this work proposes a multiple trust region-based Bayesian optimization technique(MTRBO). A trust region is a localized region within which an optimization model is trusted to approximate the objective function accurately. Assuming a Gaussian process (GP) as a prior belief about the objective function and based on the posterior mean and variance functions, the method adaptively exploits near the promising current solution inside a trust region. Also explores the most uncertain region in the search space inside another trust region. The theoretical global convergence property of the proposed method is established. Then the work is benchmarked against other state-of-the-art trust-region-based Bayesian optimization algorithms, demonstrating superior performance on a variety of non-convex and high-dimensional test functions. The proposed method outperforms others in terms of solution quality within the sampling budget (the number of function evaluations). The proposed method is applied to the portfolio optimization problem to verify its applicability in real-world scenarios.

We formulate a structural principle for finite $S_2$-objects: coherent $S_2$-sheaves and finitely generated graded $S_2$-modules decompose canonically according to the connected components in codimension $1$ of their support. This gives criteria relating indecomposability of $S_2$-objects to connectedness in codimension $1$ of their supports, and extends the Hochster--Huneke correspondences for complete local rings between connectedness in codimension $1$, indecomposability of canonical modules, and localness of the $S_2$-ifications. As a consequence, if $A$ is a local ring admitting a canonical module $ω_A$, there are canonical decompositions of both $ω_A$ and the $S_2$-ification $\operatorname{End}_A(ω_A)$ whose indecomposable summands are the canonical modules and $S_2$-ifications of the quotient rings associated to the connected components in codimension $1$. We then apply this viewpoint to the non-$S_2$ locus. For $A$ equidimensional and unmixed, this locus is naturally realized as $\operatorname{Supp}_A C$ via the $S_2$-ification sequence $0 \to A \to \operatorname{End}_A(ω_A) \to C \to 0$. The natural map between deficiency modules $K^{\dim C+1}(A)\to K^{\dim C}(C)$ identifies the canonical module $K^{\dim C}(C)$ with the $S_2$-hull of $K^{\dim C+1}(A)$. Under suitable conditions, this allows codimension-$1$ connectedness of the non-$S_2$ locus to be detected by the deficiency module $K^{\dim C+1}(A)$. We illustrate the theory with examples and apply it to codimension $2$ lattice ideals, obtaining connectedness-in-codimension-$1$ results for the non-$S_2$ loci of certain toric and lattice rings.

The two-to-two four-dimensional scattering amplitude of identical scalars obeys rigorous two-sided non-perturbative bounds derived via the modern numerical S-matrix bootstrap. These bounds carve out an allowed region with a rich boundary structure, featuring edges and vertices. In this work we further tighten this region and uncover the physics of its boundary by analyzing the asymptotic Regge behavior of the amplitude and the spectrum of resonances and virtual states. We find that the S-matrices along a given edge exhibit universal behavior, sharply contrasting with that on other edges. This reveals a classification of the boundary into distinct phases, corresponding to different UV mechanisms by which a gapped scalar arises.

This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic differential equations of the SABR model. Unlike approaches that fully replace analytical formulas with black-box models, the proposed framework preserves the analytical backbone of the model. The hybridization operates along two complementary dimensions. First, geometry-aware variables reflecting intrinsic properties of the SABR dynamics are used as structured inputs to the network. Second, the neural network is trained to learn the residual error relative to Hagan's closed-form approximation rather than implied volatility directly. The resulting model acts as a structured residual correction to the analytical formula, retaining interpretability while capturing higher-order effects that are not included in the asymptotic expansion. Numerical experiments conducted over realistic parameter domains, as well as stressed environments, show that the method improves accuracy and robustness compared with both analytical approximations and standard neural-network approaches. Because the correction remains lightweight and structurally consistent with the underlying model, the framework is well suited for real-time pricing and calibration in practical trading environments.

In this review, we establish the mathematical framework of geometrothermodynamics (GTD) as a formalism capable of describing non-extensive, quasi-homogeneous, self-gravitating systems in a Legendre-invariant manner. We argue that the fundamental equations of black holes are quasi-homogeneous functions, a property that invalidates the standard Euler identity of laboratory thermodynamics. We derive the metrics for the equilibrium manifold and analyze their curvature singularities for the Reissner-Nordström, Kerr, and Kerr-Newman black holes. Furthermore, we establish a direct correspondence between the curvature singularities of the equilibrium space and phase transitions, as determined by the divergences of the corresponding heat capacities.

The IceCube Upgrade, an extension designed to enhance the IceCube Neutrino Observatory's detection of neutrinos with energies between 1 GeV and 500 GeV, will markedly improve IceCube's sensitivity to low-mass dark matter scenarios. In this study, we present sensitivity projections for the IceCube Upgrade to neutrino fluxes arising from dark matter annihilation. In particular, we consider dark matter with masses between 3 GeV to 500 GeV from both the core of the Sun and the Galactic Center. These projections indicate that the IceCube Upgrade will enable stringent limits on dark matter in this parameter space, achieving leading sensitivities to some dark matter models with only three years of data taking.