This paper introduces a unified machine learning operations (MLOps) framework that brings ethical artificial intelligence principles into practical use by enforcing fairness, explainability, and governance throughout the machine learning lifecycle. The proposed method reduces bias by lowering the demographic parity difference (DPD) from 0.31 to 0.04 without model retuning, and cross-dataset validation achieves an area under the curve (AUC) of 0.89 on the Statlog Heart dataset. The framework maintains fairness metrics within operational limits across all deployments. Model deployment is blocked if the DPD exceeds 0.05 or if equalized odds (EO) exceeds 0.05 on the validation set. After deployment, retraining is automatically triggered if the 30-day Kolmogorov-Smirnov drift statistic exceeds 0.20. In production, the system consistently achieved DPD <= 0.05 and EO <= 0.03, while the KS statistic remained <= 0.20. Decision-curve analysis indicates a positive net benefit in the 10 to 20 percent operating range, showing that the mitigated model preserves predictive utility while satisfying fairness constraints. These results demonstrate that automated fairness gates and explainability artefacts can be successfully deployed in production without disrupting operational flow, providing organizations with a practical and credible approach to implementing ethical, transparent, and trustworthy AI across diverse datasets and operational settings.

In the past decade, advances in artificial intelligence have revolutionized sketch-based 3D modeling, leading to a new paradigm known as Deep Sketch-Based 3D Modeling (DS-3DM). DS-3DM offers data-driven methods that address the long-standing challenges of sketch abstraction and ambiguity. DS-3DM keeps humans at the center of the creative process by enhancing the flexibility, usability, faithfulness, and adaptability of sketch-based 3D modeling interfaces. This paper contributes a comprehensive survey of the latest DS-3DM within a novel design space: MORPHEUS. Built upon the Input-Model-Output (IMO) framework, MORPHEUS categorizes Models outputting Options of 3D Representations and Parts, derived from Human inputs (varying in quantity and modality), and Evaluated across diverse User-views and Styles. Throughout MORPHEUS we highlight limitations and identify opportunities for interdisciplinary research in Computer Vision, Computer Graphics, and Human-Computer Interaction, revealing a need for controllability and information-rich outputs. These opportunities align design processes more closely with user' intent, responding to the growing importance of user-centered approaches.

Modern engineering design platforms excel at discipline-specific tasks such as CAD, CAM, and CAE, but often lack native systems engineering frameworks. This creates a disconnect where system-level requirements and architectures are managed separately from detailed component design, hindering holistic development and increasing integration risks. To address this, we present the conceptual framework for the GenAI Workbench, a Model-Based Systems Engineering (MBSE) environment that integrates systems engineering principles into the designer's workflow. Built on an open-source PLM platform, it establishes a unified digital thread by linking semantic data from documents, physical B-rep geometry, and relational system graphs. The workbench facilitates an AI-assisted workflow where a designer can ingest source documents, from which the system automatically extracts requirements and uses vision-language models to generate an initial system architecture, such as a Design Structure Matrix (DSM). This paper presents the conceptual architecture, proposed methodology, and anticipated impact of this work-in-progress framework, which aims to foster a more integrated, data-driven, and informed engineering design methodology.

Partial Differential Equations are precise in modelling the physical, biological and graphical phenomena. However, the numerical methods suffer from the curse of dimensionality, high computation costs and domain-specific discretization. We aim to explore pros and cons of different PDE solvers, and apply them to specific scientific simulation problems, including forwarding solution, inverse problems and equations discovery. In particular, we extend the recent CNF (NeurIPS 2023) framework solver to coupled and non-linear settings, together with down-stream applications. The outcomes include implementation of selected methods, self-tuning techniques, evaluation on benchmark problems and a comprehensive survey of neural PDE solvers and scientific simulation applications.

We examine epistemological threats posed by human and LLM interaction. We develop collective epistemology as a theory of epistemic warrant distributed across human collectives, using bounded rationality and dual process theory as background. We distinguish internalist justification, defined as reflective understanding of why a proposition is true, from externalist justification, defined as reliable transmission of truths. Both are necessary for collective rationality, but only internalist justification produces reflective knowledge. We specify reflective knowledge as follows: agents understand the evaluative basis of a claim, when that basis is unavailable agents consistently assess the reliability of truth sources, and agents have a duty to apply these standards within their domains of competence. We argue that LLMs approximate externalist reliabilism because they can reliably transmit information whose justificatory basis is established elsewhere, but they do not themselves possess reflective justification. Widespread outsourcing of reflective work to reliable LLM outputs can weaken reflective standards of justification, disincentivize comprehension, and reduce agents' capacity to meet professional and civic epistemic duties. To mitigate these risks, we propose a three tier norm program that includes an epistemic interaction model for individual use, institutional and organizational frameworks that seed and enforce norms for epistemically optimal outcomes, and deontic constraints at organizational and or legislative levels that instantiate discursive norms and curb epistemic vices.

Wasserstein gradient flow provides a general framework for minimizing an energy functional $J$ over the space of probability measures on a Riemannian manifold $(M,g)$. Its canonical time-discretization, the Jordan-Kinderlehrer-Otto (JKO) scheme, produces for any step size $η>0$ a sequence of probability distributions $ρ_k^η$ that approximate to first order in $η$ Wasserstein gradient flow on $J$. But the JKO scheme also has many other remarkable properties not shared by other first order integrators, e.g. it preserves energy dissipation and exhibits unconditional stability for $λ$-geodesically convex functionals $J$. To better understand the JKO scheme we characterize its implicit bias at second order in $η$. We show that $ρ_k^η$ are approximated to order $η^2$ by Wasserstein gradient flow on a modified energy \[ J^η(ρ) = J(ρ) - \fracη{4}\int_M \Big\lVert \nabla_g \frac{δJ}{δρ} (ρ) \Big\rVert_{2}^{2} \,ρ(dx), \] obtained by subtracting from $J$ the squared metric curvature of $J$ times $η/4$. The JKO scheme therefore adds at second order in $η$ a deceleration in directions where the metric curvature of $J$ is rapidly changing. This corresponds to canonical implicit biases for common functionals: for entropy the implicit bias is the Fisher information, for KL-divergence it is the Fisher-Hyv{ä}rinen divergence, and for Riemannian gradient descent it is the kinetic energy in the metric $g$. To understand the differences between minimizing $J$ and $J^η$ we study JKO-Flow, Wasserstein gradient flow on $J^η$, in several simple numerical examples. These include exactly solvable Langevin dynamics on the Bures-Wasserstein space and Langevin sampling from a quartic potential in 1D.

AI agents can autonomously perform tasks and, often without explicit user consent, collect or disclose users' sensitive local data, which raises serious privacy concerns. Although AI agents' privacy policies describe their intended data practices, there remains limited transparency and accountability about whether runtime behavior matches those policies. To bridge this gap, we present AudAgent, a tool that continuously monitors AI agents' data practices in real time and guards compliance with their stated privacy policies. AudAgent comprises four components for automated privacy auditing of AI agents. (i) Policy formalization: a novel cross-LLM voting mechanism that ensures high-confidence parsing of privacy policies into formal models. (ii) Runtime annotation: a lightweight Presidio-based analyzer that detects sensitive data and annotates data practices based on the AI agent's context and the formalized privacy policy model. (iii) Compliance auditing: ontology graphs and automata-based checking that link the privacy policy model with runtime annotations, enabling on-the-fly compliance verification. (iv) User interface: an infrastructure-independent implementation that visualizes the real-time execution trace of AI agents alongside detected privacy violations, providing user-friendly transparency and accountability. We evaluate AudAgent on AI agents built with mainstream frameworks, demonstrating its effectiveness in detecting and visualizing privacy policy violations. Using AudAgent, we further find that many privacy policies lack explicit safeguards for highly sensitive data such as SSNs, whose misuse violates legal requirements, and that many agents, including those powered by Claude, Gemini, and DeepSeek,do not refuse to process such data via third-party tools. AudAgent proactively blocks operations on such data, overriding the agents' original privacy policies and behavior.

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the following up to $(1+\varepsilon)$ relative error: matrix-vector products, matrix-matrix products, the spectral norm, and sum of all entries. The runtimes of our algorithms depend on the dimension $d$, the number of points $n$, and the target error $\varepsilon$. Importantly, the dependence on $n$ in each case is far lower when accessing the kernel matrix through KDE queries as opposed to reading individual entries. Our improvements over existing best algorithms (particularly those of Backurs, Indyk, Musco, and Wagner '21) for these tasks reduce the polynomial dependence on $\varepsilon$, and additionally decreases the dependence on $n$ in the case of computing the sum of all entries of the kernel matrix. We complement our upper bounds with several lower bounds for related problems, which provide (conditional) quadratic time hardness results and additionally hint at the limits of KDE based approaches for the problems we study.

Current foundation models for electroencephalography (EEG) rely on architectures adapted from computer vision or natural language processing, typically treating neural signals as pixel grids or token sequences. This approach overlooks that the neural activity is activated by diverse sparse coding across a complex geometric topological cortex. Inspired by biological neural mechanisms, we propose the Unified Neural Topological Foundation Model (Uni-NTFM), an architecture rooted in three core neuroscience principles. In detail, to align with the brain's decoupled coding mechanism, we design the Heterogeneous Feature Projection Module. This module simultaneously encodes both time-domain non-stationary transients and frequency-domain steady-state rhythms, ensuring high quality in both waveform morphology and spectral rhythms. Moreover, we introduce a Topological Embedding mechanism to inject structured spatial priors and align different sensor configurations onto a unified latent functional topography, effectively reconstructing the geometry of brain regions. Furthermore, we achieve functional modularization and sparse coding efficiency of biological networks by constructing the Mixture-of-Experts Transformer network. This dynamic routing mechanism assigns different signal patterns and tasks to specialized neural subnetworks, and effectively preventing task interference while increasing the model capacity to record-breaking 1.9 billion parameters. Uni-NTFM is pre-trained on a diverse corpus comprising 28,000 hours of EEG data, and outperforms existing models across nine distinct downstream tasks under both linear probing and fine-tuning settings, demonstrating that aligning model architecture with neural mechanisms is significant to learn universal representations and achieve generalizable brain decoding. Our code is available at: https://anonymous.4open.science/r/Uni-NTFM-0924.

Recent advances in machine learning (ML) have accelerated progress in calibrating and operating quantum dot (QD) devices. However, most ML approaches rely on access to large, representative datasets designed to capture the full spectrum of data quality encountered in practice, with both high- and low-quality data for training, benchmarking, and validation, with labels capturing key features of the device state. Collating such datasets experimentally is challenging due to limited data availability, slow measurement bandwidths, and the labor-intensive nature of labeling. QDFlow is an open-source physics simulator for multi-QD arrays that generates realistic synthetic data with ground-truth labels. QDFlow combines a self-consistent Thomas-Fermi solver, a dynamic capacitance model, and flexible noise modules to simulate charge stability diagrams and ray-based data that closely resemble experimental results. With an extensive set of parameters that can be varied and customizable noise models, QDFlow supports the creation of large, diverse datasets for ML development, benchmarking, and quantum device research.}}

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as histopathology, topology is an important descriptor that can be used to distinguish between disease-indicating tissue by analyzing the shape characteristics of cells. Current literature suggests that reintroducing topological information using persistent homology can improve medical diagnostics; however, previous methods utilize global topological summaries which do not contain information about the locality of topological features. To address this gap, we present a novel method that generates local persistent homology-based data using a modified version of the convolution operator called \textit{Persistent Homology Convolutions}. This method captures information about the locality and translation equivariance of topological features. We perform a comparative study using various representations of histopathology slides and find that models trained with persistent homology convolutions outperform conventionally trained models and are less sensitive to hyperparameters. These results indicate that persistent homology convolutions extract meaningful geometric information from the histopathology slides.

In-Context Learning (ICL) allows Large Language Models (LLMs) to adapt to new tasks with just a few examples, but their predictions often suffer from systematic biases, leading to unstable performance in classification. While calibration techniques are proposed to mitigate these biases, we show that, in the logit space, many of these methods are equivalent to merely shifting the LLM's decision boundary without having the ability to alter its orientation. This proves inadequate when biases cause the LLM to be severely misaligned. To address these limitations and provide a unifying framework, we propose Supervised Calibration (SC), a loss-minimization-based framework, which learns an optimal, per-class affine transformation of LLM's predictive probabilities in the logit space without requiring external data beyond the context. By using a more expressive functional class, SC not only subsumes many existing calibration methods in ICL as special cases but also enables the ability of altering and even completely reversing the orientation of the LLM's decision boundary. Furthermore, SC's loss-based nature facilitates the seamless integration of two purpose-built regularization techniques, context-invariance and directional trust-region regularizers. The former is designed to tackle the instability issue in ICL, while the latter is to control the degree of calibration. Finally, SC delivers state-of-the-art performance over calibration baselines in the 4-shot, 8-shot, and 16-shot settings across all nine datasets for Mistral-7B-Instruct-v0.3, Llama-2-7B-chat, and Qwen2-7B-Instruct.

Compared to other modalities, EEG-based emotion recognition can intuitively respond to the emotional patterns in the human brain and, therefore, has become one of the most concerning tasks in the brain-computer interfaces field. Since dependencies within brain regions are closely related to emotion, a significant trend is to develop Graph Neural Networks (GNNs) for EEG-based emotion recognition. However, brain region dependencies in emotional EEG have physiological bases that distinguish GNNs in this field from those in other time series fields. Besides, there is neither a comprehensive review nor guidance for constructing GNNs in EEG-based emotion recognition. In the survey, our categorization reveals the commonalities and differences of existing approaches under a unified framework of graph construction. We analyze and categorize methods from three stages in the framework to provide clear guidance on constructing GNNs in EEG-based emotion recognition. In addition, we discuss several open challenges and future directions, such as Temporal full-connected graph and Graph condensation.

Unconditionally secure message authentication is an important part of quantum cryptography (QC). In this correspondence, we analyze security effects of using a key obtained from QC for authentication purposes in later rounds of QC. In particular, the eavesdropper gains partial knowledge on the key in QC that may have an effect on the security of the authentication in the later round. Our initial analysis indicates that this partial knowledge has little effect on the authentication part of the system, in agreement with previous results on the issue. However, when taking the full QC protocol into account, the picture is different. By accessing the quantum channel used in QC, the attacker can change the message to be authenticated. This, together with partial knowledge of the key, does incur a security weakness of the authentication. The underlying reason for this is that the authentication used, which is insensitive to such message changes when the key is unknown, becomes sensitive when used with a partially known key. We suggest a simple solution to this problem, and stress usage of this or an equivalent extra security measure in QC.

Preference aggregation in a multiagent setting is a central issue in both human and computer contexts. In this paper, we study in terms of complexity the vulnerability of preference aggregation to destructive control. That is, we study the ability of an election's chair to, through such mechanisms as voter/candidate addition/suppression/partition, ensure that a particular candidate (equivalently, alternative) does not win. And we study the extent to which election systems can make it impossible, or computationally costly (NP-complete), for the chair to execute such control. Among the systems we study--plurality, Condorcet, and approval voting--we find cases where systems immune or computationally resistant to a chair choosing the winner nonetheless are vulnerable to the chair blocking a victory. Beyond that, we see that among our studied systems no one system offers the best protection against destructive control. Rather, the choice of a preference aggregation system will depend closely on which types of control one wishes to be protected against. We also find concrete cases where the complexity of or susceptibility to control varies dramatically based on the choice among natural tie-handling rules.

Among the most compelling cold dark matter candidates, the axion has recently been subject to a wide range of astrophysical studies aiming to constraints its properties. We present updated bounds on the isocurvature fraction, $f_{\rm{iso}}$, which parameterizes the contribution of isocurvature perturbations induced by post-inflationary produced axion-like particles (ALPs) to the ordinary power spectrum. We use new simulations based on the Sherwood-Relics suite to fit high-resolution Lyman-$α$ forest flux power spectrum data. With the published noise model of the Lyman-$α$ forest data, we find a tentative detection of $f_{\rm{iso}}$ = ${0.0064^{+0.0012}_{-0.0014}}$ (68% C.L), after accounting for the degenerate effect of IGM thermal evolution. With a more conservative modelling of the residual noise in the data, the upper bound is weakened to $f_{\rm{iso}}< 0.0084$ (95% C.L), which translates into an ALP temperature-independent mass $m_a > 1.73 \times 10^{-18}$eV. Our constraints are stronger than bounds derived from large-scale structure probes at higher and lower redshifts and are competitive with those derived from UV luminosity function data. Interestingly, the best current Lyman-$α$ forest data prefers a non-zero contribution from isocurvature modes.

We investigate the effects, stability, and nonlinear dynamics of ghost scalar matter modeled as a field with a negative kinetic term confined within the cores of neutron stars. To this end, we analyze static configurations of the coupled Einstein-Euler-(ghost, complex) Klein-Gordon system and then we perform fully dynamical numerical evolutions of illustrative cases. Our results demonstrate that neutron stars can gravitationally confine a finite amount of ghost matter and support continuous families of equilibrium solutions, indicating that these configurations are not the result of fine tuning. We analyze the properties of the final states and find that the neutron star undergoes a persistent pulse-like oscillatory motion. In particular, we explicitly compute the frequency synchronization between the stellar fluid oscillation modes and those of the ghost scalar sector.

Hybrid continuous-variable (CV)-discrete-variable (DV) quantum systems present a promising direction for quantum computing by combining the high dimensional encoding capabilities of qumodes with the control offered by DV qubits on the coupled qumodes. There have been exciting recent progresses on hybrid CV-DV quantum computing, including variational algorithms, error correction, compiler-level optimizations for Hamiltonian simulation, etc. However, there is a lack of a standardized CV-DV benchmark suite for assessing various emerging hardware platforms and evaluating software optimizations on hybrid CV-DV circuits. In this work, we introduce a simulation and benchmarking framework for hybrid CV-DV circuits, implemented using Bosonic Qiskit-a tool specifically designed to model CV-DV systems, along with QuTip for functional correctness verification. We construct and characterize representative CV-DV benchmarks, including cat state generation, GKP state generation, CV-DV state transfers, hybrid quantum Fourier transform, variational quantum algorithms, Hamiltonian simulation, and Shor's algorithm. To assess circuit complexity and scalability, we define a feature map organized into two categories: general features (e.g., qubit/qumode count, gate counts) and CV-DV-specific features (e.g., Wigner negativity, energy, truncation cost). These metrics enable evaluation of both classical simulability and hardware resource requirements. Our results, including one benchmark on real hardware, demonstrate that hybrid CV-DV architectures are not only viable but well-suited for a range of computational tasks, from optimization to Hamiltonian simulation. This framework lays the groundwork for systematic evaluation and future development of hybrid quantum systems.

A complete picture of the gas thermodynamics around galaxies is imprinted on the cosmic microwave background (CMB). Indeed, the thermal, kinematic, and relativistic Sunyaev-Zel'dovich effects (tSZ, kSZ, rSZ) measure the gas density, temperature, pressure of baryonic feedback and bulk velocity around galaxies, along with the gravitational potential it sits in. This full thermodynamic picture promises to constrain galaxy formation models and gas related uncertainties in the impact on galaxy lensing. Recent kSZ measurements around galaxies suggest that the gas may be more extended than anticipated, pointing to powerful feedback processes and large baryonic corrections to lensing. How robust are these conclusions about the galaxy-halo connection, including satellite fraction and high-mass outliers, or to 2D projection effects and large-scale velocity modes? In this paper, we give estimates for these effects using a simulated sample of DESI-like luminous red galaxies within the IllustrisTNG hydrodynamical simulation and the Abacus N-body simulation. We show that analyzing projected 2D profiles can lead to biases when computing quantities like the gas fraction. We also find that in the absence of spatial filtering, the 2-halo term is non-negligible for kSZ even at the smaller radii where the 1-halo term dominates. We show that a 1% uncertainty in the satellite fraction of galaxies can propagate into uncertainties of $\pm$1%, $\pm$3% and $\pm$5% in the 1-halo terms of the kSZ, tSZ, and rSZ signals, respectively. We show that masking the 2% most massive objects in the sample reduces the profile amplitudes by up to 10%, 40%, and 75% for the kSZ, tSZ, and rSZ signals, respectively. Finally, we show that naive simulations of the kSZ effect can be biased by an artificial Doppler term, which is automatically removed when high-pass or compensated aperture filtering is applied.

Many research works have concerned normality-preserving selection rules and operations on the sequence of digits of a given normal number that maintain or violate normality. This leads us to introduce rearrangement operations on finite subwords appearing within the digit expansions of normal numbers, and this is inspired by the concept of an abelian complexity function in the field of combinatorics on words. We introduce the concept of an abelian-normal number, with respect to a given base and a given weighting/counting function on subwords, by analogy with normal numbers and with the use of the equivalence classes associated with abelian complexity functions. We then construct a non-normal analogue $D_{10}$ of Champernowne's constant $C_{10}$ and prove that $D_{10}$ is abelian-normal with respect to a given weighting function. We conclude with two open problems concerning our Champernowne-like constant $D_{10}$.

In this work, we present bayesgrid, an open-source python toolbox for generating synthetic power transmission-distribution systems for any geographical location worldwide, using the publicly available data from OpenStreetMap (OSM). The toolbox is based on Bayesian Hierarchical Models (BHM) which is trained on existing distribution network databases to develop a probabilistic model and can be applied to any geographical location worldwide, leveraging transfer learning. Thanks to the BHM, the tool is capable of generating multiple instances of the distribution system for a same region. The generated networks contain three-phase phase-consistent unbalanced networks, radial topology and information on the nodal demand distributions. The generated network also contain the critical reliability indices, specifically the interruption duration and frequency of failure for individual grid components, allowing its application in reliability-related studies. The tool is demonstrated for different case studies generating synthetic network datasets for different geographical regions around the world. The framework allows saving the generated networks into open-source platforms: PandaPower and OpenDSS. We also present an application for computation of probabilistic hosting capacity using the synthetic networks.

This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras for type $(1, 2).$ For each obtained algebra, we describe the derivation algebra, the automorphism group, the lattice of subalgebras and ideals, and functional identities of degree $2$. Furthermore, we investigate the Allison-Kantor construction for the classified algebras. We determine the structure of the resulting $\mathbb{Z}$-graded Lie algebras, providing their dimensions and Levi decompositions.

Hyperuniform disorder is a type of correlated disorder characterized by vanishing spectral density at small wavevectors, making the configuration effectively homogeneous on long length scales. In photonics, hyperuniform disorder is promising for generating isotropic photonic pseudogaps and engineering photonic crystal waveguides. However, these studies are largely restricted to idealized lossless settings, although all photonic systems necessarily have loss. In this work, light propagation in photonic crystal slabs with imposed hyperuniform disorder is investigated theoretically and numerically. The system is intrinsically non-Hermitian due to radiative loss, with non-Hermiticity appearing as a complex effective mass of a quadratic photonic band. A theoretical framework for disorder scattering is analytically derived in Hermitian and non-Hermitian quadratic bands with real and complex effective mass, respectively. In contrast to the power law behavior $|\mathbf{k}|^α$ observed in the Hermitian case (where $α$ is the hyperuniformity exponent), the scattering loss in the non-Hermitian band is given by $C_0+C_{β_2}\cdot|\mathbf{k}|^{β_2}$, where $C_0$ is a finite constant and the exponent $β_2\leq 2$. Our theoretical predictions are verified with tight-binding and Finite-Difference Time-Domain simulations with realistic photonic crystal parameters, based on recent experiments.

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations over an algebra. Such an existence occurs when an algebra is non-domestic; a conjecture due to M. Prest. G. Puniski confirms the conjecture for non-domestic string algebras. Geiß, Labardini-Fragoso and Schröer show that every Jacobian algebra associated with a triangulation of a closed surface with marked points is finite-dimensional and tame. We show that, excluding only the case of a sphere with four (or fewer) punctures, there exists a special family of pointed modules, called an independent pair of dense chains of pointed modules. In the process, we show the existence of such an independent pair in a non-domestic skew-gentle algebra and (skew) Brauer graph algebras by showing that the Galois semi-covering functor and trivial extension preserve such pairs. Then it follows from a result of M. Ziegler that there exists a superdecomposable pure-injective module if the algebraically closed field is countable.

We show that for any infinite tree of finite cone type satisfying a mild expansion condition, the only typical process on its vertices with covariance induced by the Green's function is the Gaussian wave. This generalizes a result of Backhausz and Szegedy, who proved this for the infinite regular tree of degree $d\geq 3$. We do this by giving a reduction to a statement concerning the distribution of the inner product of our process with columns of the Green's function, which in turn are straightforward to calculate. As a consequence, for random bipartite biregular graphs, the distribution of local neighborhoods of eigenvectors must approximate the Gaussian wave. Moreover, for generic configuration models including random lifts, the local distribution of a uniformly chosen eigenvector from any arbitrarily small spectral window likewise converges to the Gaussian wave.

We present a novel method for constructing high-accuracy, time-varying disk-integrated stellar absorption line profiles that isolate the effects of granulation alone. This framework provides an effectively unlimited supply of physically consistent training data, offering a unique opportunity to study granulation-driven velocity variability with no contamination from other stellar processes or instrumental systematics. Our interpolation scheme enables accurate profile generation at arbitrary limb angles and successfully reproduces observed disk integrated solar bisector shapes from IAG spectra. Using four Fe I lines (525.0, 615.2, 617.3, and 627.1 nm), we produce 1000 model star disk-integrated realisations per line and find an isolated granulation-induced RV scatter of 0.16-0.21 m s^-1. Using our synthetic profiles and assuming infinite signal-to-noise, we find strong correlations between various line-shape metrics and convective blueshift, demonstrating that line-shape diagnostics can, in principle, trace granulation effects. Equivalent width proves the strongest diagnostic, achieving up to 60% scatter reduction. However, the strength of all simple line shape diagnostics rapidly diminishes once photon noise is injected. Even when artificially boosting the signal to represent a spectrum containing ~1000 spectral lines, the achievable improvement with these metrics remains below 10% at typical signal-to-noise ratios. Our results highlight the need for more robust, noise-resilient diagnostics and position our synthetic dataset as a valuable testbed for developing and benchmarking such methods.

Low Latency, Low Loss, and Scalable Throughput (L4S) is an emerging paradigm for latency control based on DualPI2 active queue management and scalable congestion control. While a Linux kernel implementation of DualPI2 is available, controlled and reproducible experimentation on L4S mechanisms can be facilitated by a modular, user-space alternative. In this paper, we present a DualPI2 module for the Mahimahi network emulator, designed to support extensible, component-level experimentation without kernel modification. We conduct a statistical behavioral characterization of the Mahimahi implementation by examining key metrics across diverse traffic patterns and network conditions, using the Linux kernel implementation as a reference baseline. Our analysis shows that behavioral alignment across execution environments is not automatic: identical DualPI2 parameterization does not guarantee identical dynamics. Instead, key control parameters exhibit environment-dependent sensitivity, leading to regime-dependent discrepancies across bandwidth-delay product (BDP) conditions. Through targeted parameter exploration, we identify configurations that improve cross-platform alignment in low BDP regimes, while revealing structural differences that persist under higher load. This work provides both a practical tool for experimental L4S research and empirical insight into cross-platform behavioral differences, highlighting the importance of systematic characterization and environment-aware parameter selection in emulation-based AQM studies.

We formalize in Lean the following foundational result in commutative algebra: Let $R \to S$ be a faithfully flat map of (not necessarily noetherian) commutative rings, and let $P$ be an arbitrary $R$-module. Then $P$ is projective over $R$ if and only if $S\otimes_R P$ is projective over $S$. This formalizes and verifies Perry's fix of a subtle gap in the classical work of Raynaud and Gruson, a result which is a key ingredient in the study of finitistic dimension of commutative noetherian rings.

Hermiticity is usually treated as a foundational axiom of quantum mechanics, guaranteeing real spectra and unitary time evolution. In this work we argue that Hermiticity is more naturally understood as a symmetry law arising from the global conservation of an inner product current. We show that in spacetimes admitting complete Cauchy surfaces without boundary flux this conservation reduces to the familiar Hermiticity condition of the canonical inner product. However, in the presence of causal horizons, most strikingly in black hole geometries, this conservation law becomes obstructed for restricted observers. Tracing over inaccessible degrees of freedom then inevitably yields completely positive trace preserving dynamics with an effective non-Hermitian generator. Using quantum thermodynamics and the monotonicity of relative entropy, we demonstrate that the generalized second law may be reinterpreted as an entropy balance that compensates precisely for the flux of inner product charge through the horizon. The structure of Einstein equations, through the Bianchi identity and the Raychaudhuri focusing equation, provides the geometric mechanism underlying this balance. We also show that black hole ringdown can serve as a realistic observational probe of this idea and may provide quantitative upper bounds on the strength of horizon-induced inner product flux. In this way gravity, entropy production, and effective non-Hermiticity are unified under a single structural principle, with Hermiticity emerging as the special case of globally conserved inner product symmetry.

The study of Stark broadening of neutral helium lines, despite significant advances over recent decades, has not led to updated large grids of helium line profiles relevant to the spectroscopic study of helium-rich stars. While the semi-analytical approach based on the standard Stark broadening theory is efficient for generating such grids, it presents challenges in incorporating additional physical effects into the model. Motivated by recent studies that highlight potential issues with line profiles in the context of white dwarf stars, this paper leverages advances in computer simulations to create a new grid of line profiles for 13 neutral helium lines in the optical range. These profiles cover densities ranging from 10^14 to 6 x 10^17 cm^-3 and temperatures from 10,000 K to 40,000 K, with the exception of the narrower He I 4713 line, for which the profile grid begins at 10^15.5 cm^-3. The primary goal of this research is to present the new grid and compare it with both the semi-analytical approach and other simulation results. By doing so, corrections to the previous grid will be explored, providing a foundation for future studies that utilize this updated grid. We also examine the impact of these new profiles on the determination of physical parameters for a range of astrophysical objects, including DB white dwarfs and other helium-rich stars.