Boosting has garnered significant interest across both machine learning and statistical communities. Traditional boosting algorithms, designed for fully observed random samples, often struggle with real-world problems, particularly with interval-censored data. This type of data is common in survival analysis and time-to-event studies where exact event times are unobserved but fall within known intervals. Effective handling of such data is crucial in fields like medical research, reliability engineering, and social sciences. In this work, we introduce novel nonparametric boosting methods for regression and classification tasks with interval-censored data. Our approaches leverage censoring unbiased transformations to adjust loss functions and impute transformed responses while maintaining model accuracy. Implemented via functional gradient descent, these methods ensure scalability and adaptability. We rigorously establish their theoretical properties, including optimality and mean squared error trade-offs. Our proposed methods not only offer a robust framework for enhancing predictive accuracy in domains where interval-censored data are common but also complement existing work, expanding the applicability of existing boosting techniques. Empirical studies demonstrate robust performance across various finite-sample scenarios, highlighting the practical utility of our approaches.

Foundation Models (FMs) have surged in popularity over the past five years, with applications spanning fields from computer vision to natural language processing. Brain-Computer Interfaces (BCIs) have also gained momentum due to their potential to support individuals with complex disabilities. Among BCI paradigms, code-modulated Visual Evoked Potentials (c-VEPs) remain relatively understudied, despite offering high information transfer rates and large selection target capacities. However, c-VEP systems require lengthy calibration sessions, limiting their practicality outside of laboratory settings. In this study, we use a FM for the first time to eliminate the need for lengthy calibration in c-VEP BCI systems. We evaluated two approaches: (1) a truly calibration-free approach requiring no subject-specific data, and (2) a limited calibration approach, where we assessed the benefit of incorporating incremental amounts of calibration data. In both cases, a classification head is trained on data from other subjects. For a new subject, no calibration data is required in the calibration-free setup, making the c-VEP system effectively plug-and-play. The proposed method was tested on two c-VEP datasets. For the calibration-free approach, the average accuracy on the first dataset (n = 17) was 68.8% +/- 17.6%, comparable to the full-calibration performance reported in the original study (66.2% +/- 13.8%), which required approximately 11 minutes of calibration. On the second dataset (n = 12), the calibration-free accuracy was 71.8% +/- 20.2%, versus 93.7% +/- 5.5% from the original study, which required around 3.5 minutes. A limited-calibration approach using only 20% of the subject's data (approximately 43 seconds) yielded 92% +/- 5.2% accuracy. These results indicate that our FM-based approach can effectively eliminate or significantly reduce the need for lengthy calibration in c-VEP BCIs.

Fairness in algorithmic decision-making is often framed in terms of individual fairness, which requires that similar individuals receive similar outcomes. A system violates individual fairness if there exists a pair of inputs differing only in protected attributes (such as race or gender) that lead to significantly different outcomes-for example, one favorable and the other unfavorable. While this notion highlights isolated instances of unfairness, it fails to capture broader patterns of systematic or clustered discrimination that may affect entire subgroups. We introduce and motivate the concept of discrimination clustering, a generalization of individual fairness violations. Rather than detecting single counterfactual disparities, we seek to uncover regions of the input space where small perturbations in protected features lead to k-significantly distinct clusters of outcomes. That is, for a given input, we identify a local neighborhood-differing only in protected attributes-whose members' outputs separate into many distinct clusters. These clusters reveal significant arbitrariness in treatment solely based on protected attributes that help expose patterns of algorithmic bias that elude pairwise fairness checks. We present HyFair, a hybrid technique that combines formal symbolic analysis (via SMT and MILP solvers) to certify individual fairness with randomized search to discover discriminatory clusters. This combination enables both formal guarantees-when no counterexamples exist-and the detection of severe violations that are computationally challenging for symbolic methods alone. Given a set of inputs exhibiting high k-unfairness, we introduce a novel explanation method to generate interpretable, decision-tree-style artifacts. Our experiments demonstrate that HyFair outperforms state-of-the-art fairness verification and local explanation methods.

Future intelligent indoor wireless environments require fast and reliable beam alignment to sustain high-throughput links under mobility and blockage. Exhaustive beam training achieves optimal performance but is prohibitively costly. In indoor settings, dense scatterers and transceiver hardware imperfections introduce multipath and sidelobe leakage, producing measurable power across multiple angles and reducing the effectiveness of outdoor-oriented alignment algorithms. This paper presents a Refined Bayesian Optimization (R-BO) framework that exploits the inherent structure of mmWave transceiver patterns, where received power gradually increases as the transmit and receive beams converge toward the optimum. R-BO integrates a Gaussian Process (GP) surrogate with a Matern kernel and an Expected Improvement (EI) acquisition function, followed by a localized refinement around the predicted optimum. The GP hyperparameters are re-optimized online to adapt to irregular variations in the measured angular power field caused by reflections and sidelobe leakage. Experiments across 43 receiver positions in an indoor laboratory demonstrate 97.7% beam-alignment accuracy within 10 degrees, less than 0.3 dB average loss, and an 88% reduction in probing overhead compared to exhaustive search. These results establish R-BO as an efficient and adaptive beam-alignment solution for real-time intelligent indoor wireless environments.

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, $\ell_2$ or $\ell_1$ methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

Data-driven approaches using deep learning are emerging as powerful techniques to extract non-Gaussian information from cosmological large-scale structure. This work presents the first simulation-based inference (SBI) pipeline that combines weak lensing and galaxy clustering maps in a realistic Dark Energy Survey Year 3 (DES Y3) configuration and serves as preparation for a forthcoming analysis of the survey data. We develop a scalable forward model based on the CosmoGridV1 suite of N-body simulations to generate over one million self-consistent mock realizations of DES Y3 at the map level. Leveraging this large dataset, we train deep graph convolutional neural networks on the full survey footprint in spherical geometry to learn low-dimensional features that approximately maximize mutual information with target parameters. These learned compressions enable neural density estimation of the implicit likelihood via normalizing flows in a ten-dimensional parameter space spanning cosmological $w$CDM, intrinsic alignment, and linear galaxy bias parameters, while marginalizing over baryonic, photometric redshift, and shear bias nuisances. To ensure robustness, we extensively validate our inference pipeline using synthetic observations derived from both systematic contaminations in our forward model and independent Buzzard galaxy catalogs. Our forecasts yield significant improvements in cosmological parameter constraints, achieving $2-3\times$ higher figures of merit in the $Ω_m - S_8$ plane relative to our implementation of baseline two-point statistics and effectively breaking parameter degeneracies through probe combination. These results demonstrate the potential of SBI analyses powered by deep learning for upcoming Stage-IV wide-field imaging surveys.

We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that the scaling limits of SGD-M coincide with those of online SGD after an appropriate time rescaling and a specific choice of step-size. However, if the step-size is kept the same between the two algorithms, SGD-M will amplify high-dimensional effects, potentially degrading performance relative to online SGD. We demonstrate our framework on two popular learning problems: Spiked Tensor PCA and Single Index Models. In both cases, we also examine online SGD with an adaptive step-size based on normalized gradients. In the high-dimensional regime, this algorithm yields multiple benefits: its dynamics admit fixed points closer to the population minimum and widens the range of admissible step-sizes for which the iterates converge to such solutions. These examples provide a rigorous account, aligning with empirical motivation, of how early preconditioners can stabilize and improve dynamics in settings where online SGD fails.

Accurate vibration measurement is vital for analyzing dynamic systems across science and engineering, yet noncontact methods often balance precision against practicality. Event cameras offer high-speed, low-light sensing, but existing approaches fail to recover vibration amplitude and frequency with sufficient accuracy. We present an event topology-based visual microphone that reconstructs vibrations directly from raw event streams without external illumination. By integrating the Mapper algorithm from topological data analysis with hierarchical density-based clustering, our framework captures the intrinsic structure of event data to recover both amplitude and frequency with high fidelity. Experiments demonstrate substantial improvements over prior methods and enable simultaneous recovery of multiple sound sources from a single event stream, advancing the frontier of passive, illumination-free vibration sensing.

A central challenge in cognitive neuroscience is to explain how semantic and episodic memory, two major forms of declarative memory, typically associated with cortical and hippocampal processing, interact to support learning, recall, and imagination. Despite significant advances, we still lack a unified computational framework that jointly accounts for core empirical phenomena across both semantic and episodic processing domains. Here, we introduce the Generative Episodic-Semantic Integration System (GENESIS), a computational model that formalizes memory as the interaction between two limited-capacity generative systems: a Cortical-VAE, supporting semantic learning and generalization, and a Hippocampal-VAE, supporting episodic encoding and retrieval within a retrieval-augmented generation (RAG) architecture. GENESIS reproduces hallmark behavioral findings, including generalization in semantic memory, recognition, serial recall effects and gist-based distortions in episodic memory, and constructive episodic simulation, while capturing their dynamic interactions. The model elucidates how capacity constraints shape the fidelity and memorability of experiences, how semantic processing introduces systematic distortions in episodic recall, and how episodic replay can recombine previous experiences. Together, these results provide a principled account of memory as an active, constructive, and resource-bounded process. GENESIS thus advances a unified theoretical framework that bridges semantic and episodic memory, offering new insights into the generative foundations of human cognition.

Time series foundation models (TSFMs) are increasingly being adopted as highly-capable general-purpose time series representation learners. Although their training corpora are vast, they exclude astronomical time series data. Observations of stars produce peta-scale time series with unique challenges including irregular sampling and heteroskedasticity. We introduce StarEmbed, the first public benchmark for rigorous and standardized evaluation of state-of-the-art TSFMs on stellar time series observations (``light curves''). We benchmark on three scientifically-motivated downstream tasks: unsupervised clustering, supervised classification, and out-of-distribution source detection. StarEmbed integrates a catalog of expert-vetted labels with multi-variate light curves from the Zwicky Transient Facility, yielding ~40k hand-labeled light curves spread across seven astrophysical classes. We evaluate the zero-shot representation capabilities of three TSFMs (MOIRAI, Chronos, Chronos-Bolt) and a domain-specific transformer (Astromer) against handcrafted feature extraction, the long-standing baseline in the astrophysics literature. Our results demonstrate that these TSFMs, especially the Chronos models, which are trained on data completely unlike the astronomical observations, can outperform established astrophysics-specific baselines in some tasks and effectively generalize to entirely new data. In particular, TSFMs deliver state-of-the-art performance on our out-of-distribution source detection benchmark. With the first benchmark of TSFMs on astronomical time series data, we test the limits of their generalization and motivate a paradigm shift in time-domain astronomy from using task-specific, fully supervised pipelines toward adopting generic foundation model representations for the analysis of peta-scale datasets from forthcoming observatories.

Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In this work, we propose Conditionally Whitened Generative Models (CW-Gen), a framework that incorporates prior information through conditional whitening. Theoretically, we establish sufficient conditions under which replacing the traditional terminal distribution of diffusion models, namely the standard multivariate normal, with a multivariate normal distribution parameterized by estimators of the conditional mean and covariance improves sample quality. Guided by this analysis, we design a novel Joint Mean-Covariance Estimator (JMCE) that simultaneously learns the conditional mean and sliding-window covariance. Building on JMCE, we introduce Conditionally Whitened Diffusion Models (CW-Diff) and extend them to Conditionally Whitened Flow Matching (CW-Flow). Experiments on five real-world datasets with six state-of-the-art generative models demonstrate that CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches. Empirical results further demonstrate that CW-Gen can effectively mitigate the effects of distribution shift.

Pre-trained models (PTMs) are machine learning models that have been trained in advance, often on large-scale data, and can be reused for new tasks, thereby reducing the need for costly training from scratch. Their widespread adoption introduces a new class of software dependency, which we term Software Dependencies 2.0, extending beyond conventional libraries to learned behaviors embodied in trained models and their associated artifacts. The integration of PTMs as software dependencies in real projects remains unclear, potentially threatening maintainability and reliability of modern software systems that increasingly rely on them. Objective: In this study, we investigate Software Dependencies 2.0 in open-source software (OSS) projects by examining the reuse of PTMs, with a focus on how developers manage and integrate these models. Specifically, we seek to understand: (1) how OSS projects structure and document their PTM dependencies; (2) what stages and organizational patterns emerge in the reuse pipelines of PTMs within these projects; and (3) the interactions among PTMs and other learned components across pipeline stages. We conduct a mixed-methods analysis of a statistically significant random sample of 401 GitHub repositories from the PeaTMOSS dataset (28,575 repositories reusing PTMs from Hugging Face and PyTorch Hub). We quantitatively examine PTM reuse by identifying patterns and qualitatively investigate how developers integrate and manage these models in practice.

Noise in low-dose computed tomography (LDCT) can obscure important diagnostic details. While deep learning offers powerful denoising, supervised methods require impractical paired data, and self-supervised alternatives often use opaque, parameter-heavy networks that limit clinical trust. We propose Filter2Noise (F2N), a novel self-supervised framework for interpretable, zero-shot denoising from a single LDCT image. Instead of a black-box network, its core is an Attention-Guided Bilateral Filter, a transparent, content-aware mathematical operator. A lightweight attention module predicts spatially varying filter parameters, making the process transparent and allowing interactive radiologist control. To learn from a single image with correlated noise, we introduce a multi-scale self-supervised loss coupled with Euclidean Local Shuffle (ELS) to disrupt noise patterns while preserving anatomical integrity. On the Mayo Clinic LDCT Challenge, F2N achieves state-of-the-art results, outperforming competing zero-shot methods by up to 3.68 dB in PSNR. It accomplishes this with only 3.6k parameters, orders of magnitude fewer than competing models, which accelerates inference and simplifies deployment. By combining high performance with transparency, user control, and high parameter efficiency, F2N offers a trustworthy solution for LDCT enhancement. We further demonstrate its applicability by validating it on clinical photon-counting CT data. Code is available at: https://github.com/sypsyp97/Filter2Noise.

We propose a demand estimation approach that leverages unstructured data to infer substitution patterns. Using pre-trained deep learning models, we extract embeddings from product images and textual descriptions and incorporate them into a mixed logit demand model. This approach enables demand estimation even when researchers lack data on product attributes or when consumers value hard-to-quantify attributes such as visual design. Using a choice experiment, we show this approach substantially outperforms standard attribute-based models at counterfactual predictions of second choices. We also apply it to 40 product categories offered on Amazon.com and consistently find that unstructured data are informative about substitution patterns.

Alignment in large language models (LLMs) is used to enforce guidelines such as safety. Yet, alignment fails in the face of jailbreak attacks that modify inputs to induce unsafe outputs. In this paper, we introduce and evaluate a new technique for jailbreak attacks. We observe that alignment embeds a safety classifier in the LLM responsible for deciding between refusal and compliance, and seek to extract an approximation of this classifier: a surrogate classifier. To this end, we build candidate classifiers from subsets of the LLM. We first evaluate the degree to which candidate classifiers approximate the LLM's safety classifier in benign and adversarial settings. Then, we attack the candidates and measure how well the resulting adversarial inputs transfer to the LLM. Our evaluation shows that the best candidates achieve accurate agreement (an F1 score above 80%) using as little as 20% of the model architecture. Further, we find that attacks mounted on the surrogate classifiers can be transferred to the LLM with high success. For example, a surrogate using only 50% of the Llama 2 model achieved an attack success rate (ASR) of 70% with half the memory footprint and runtime -- a substantial improvement over attacking the LLM directly, where we only observed a 22% ASR. These results show that extracting surrogate classifiers is an effective and efficient means for modeling (and therein addressing) the vulnerability of aligned models to jailbreaking attacks. The code is available at https://github.com/jcnf0/targeting-alignment.

As AI agents take on increasingly long-running tasks involving sophisticated planning and execution, there is a corresponding need for novel interaction designs that enable deeper human-agent collaboration. However, most prior works leverage human interaction to fix "autonomous" workflows that have yet to become fully autonomous or rigidly treat planning and execution as separate stages. Based on a formative study with 9 researchers using AI to support their work, we propose a design that affords greater flexibility in collaboration, so that users can 1) delegate agency to the user or agent via a collaborative plan where individual steps can be assigned; and 2) interleave planning and execution so that plans can adjust after partial execution. We introduce Cocoa, a system that takes design inspiration from computational notebooks to support complex research tasks. A lab study (n=16) found that Cocoa enabled steerability without sacrificing ease-of-use, and a week-long field deployment (n=7) showed how researchers collaborated with Cocoa to accomplish real-world tasks.

In federated learning (FL), data providers jointly train a machine learning model without sharing their training data. This makes it challenging to provide verifiable claims about the trained FL model, e.g., related to the employed training data, any data sanitization, or the correct training algorithm-a malicious data provider can simply deviate from the correct training protocol without detection. While prior FL training systems have explored the use of trusted execution environments (TEEs) to protect the training computation, such approaches rely on the confidentiality and integrity of TEEs. The confidentiality guarantees of TEEs, however, have been shown to be vulnerable to a wide range of attacks, such as side-channel attacks. We describe VerifiableFL, a system for training FL models that establishes verifiable claims about trained FL models with the help of fine-grained runtime attestation proofs. Since these runtime attestation proofs only require integrity protection, VerifiableFL generates them using the new abstraction of exclaves. Exclaves are integrity-only execution environments, which do not contain software-managed secrets and thus are immune to data leakage attacks. VerifiableFL uses exclaves to attest individual data transformations during FL training without relying on confidentiality guarantees. The runtime attestation proofs then form an attested dataflow graph of the entire FL model training computation. The graph is checked by an auditor to ensure that the trained FL model satisfies its claims, such as the use of data sanitization by data providers or correct aggregation by the model provider. VerifiableFL extends NVFlare FL framework to use exclaves. We show that VerifiableFL introduces less than 12% overhead compared to unprotected FL training.

P300 speller BCIs allow users to compose sentences by selecting target keys on a GUI through the detection of P300 component in their EEG signals following visual stimuli. Most P300 speller BCIs require users to spell words letter by letter, or the first few initial letters, resulting in high keystroke demands that increase time, cognitive load, and fatigue. This highlights the need for more efficient, user-friendly methods for faster sentence composition. In this work, we introduce ChatBCI, a P300 speller BCI that leverages the zero-shot learning capabilities of large language models (LLMs) to suggest words from user-spelled initial letters or predict the subsequent word(s), reducing keystrokes and accelerating sentence composition. ChatBCI retrieves word suggestions through remote queries to the GPT-3.5 API. A new GUI, displaying GPT-3.5 word suggestions as extra keys is designed. SWLDA is used for the P300 classification. Seven subjects completed two online spelling tasks: 1) copy-spelling a self-composed sentence using ChatBCI, and 2) improvising a sentence using ChatBCI's word suggestions. Results demonstrate that in Task 1, on average, ChatBCI outperforms letter-by-letter BCI spellers, reducing time and keystrokes by 62.14% and 53.22%, respectively, and increasing information transfer rate by 198.96%. In Task 2, ChatBCI achieves 80.68% keystroke savings and a record 8.53 characters/min for typing speed. Overall, ChatBCI, by employing remote LLM queries, enhances sentence composition in realistic scenarios, significantly outperforming traditional spellers without requiring local model training or storage. ChatBCI's (multi-) word predictions, combined with its new GUI, pave the way for developing next-generation speller BCIs that are efficient and effective for real-time communication, especially for users with communication and motor disabilities.

A light field image captures scenes through its micro-lens array, providing a rich representation that encompasses spatial and angular information. While this richness comes at significant data redundancy, most existing methods tend to indiscriminately utilize all the information from sub-aperture images (SAIs) in an attempt to harness every visual cue regardless of their disparity significance. However, this paradigm inevitably leads to disparity entanglement, a fundamental cause of inefficiency in light field image processing. To address this limitation, we introduce the Skim Transformer, a novel architecture inspired by the "less is more" philosophy. It features a multi-branch structure where each branch is dedicated to a specific disparity range by constructing its attention score matrix over a skimmed subset of SAIs, rather than all of them. Building upon it, we present SkimLFSR, an efficient yet powerful network for light field image super-resolution. Requiring only 67% of the prior leading method's parameters}, SkimLFSR achieves state-of-the-art results surpassing the best existing method by 0.63 dB and 0.35 dB PSNR at the 2x and 4x tasks, respectively. Through in-depth analyses, we reveal that SkimLFSR, guided by the predefined skimmed SAI sets as prior knowledge, demonstrates distinct disparity-aware behaviors in attending to visual cues. Last but not least, we conduct an experiment to validate SkimLFSR's generalizability across different angular resolutions, where it achieves competitive performance on a larger angular resolution without any retraining or major network modifications. These findings highlight its effectiveness and adaptability as a promising paradigm for light field image processing.

Recent algorithmic advances have made equality saturation an appealing approach to program optimization because it avoids the phase-ordering problem. Existing work uses external equality saturation libraries, or custom implementations that are deeply tied to the specific application. However, these works only apply equality saturation at a single level of abstraction, or discard the discovered equalities when code is transformed by other compiler passes. We propose an alternative approach that represents an e-graph natively in the compiler's intermediate representation, facilitating the application of constructive compiler passes that maintain the e-graph state throughout the compilation flow. We build on a Python-based MLIR framework, xDSL, and introduce a new MLIR dialect, eqsat, that represents e-graphs in MLIR code. We show that this representation expands the scope of equality saturation in the compiler, allowing us to interleave pattern rewriting with other compiler transformations. The eqsat dialect provides a unified abstraction for compilers to utilize equality saturation across various levels of intermediate representations concurrently within the same MLIR flow.

Motivated by observational evidence from JWST and theoretical results from cosmological simulations, we use a simple parametric, phenomenological model to test to what extent bursty star formation with standard Initial Mass Function, no continuous star formation, no mergers, \mr{and no dust} can account for the observed properties in the $M_{UV}$ vs $M_*$ plane of galaxies at redshifts $z>5$. We find that the simplest model that fits the data has a quiescence period between bursts $Δt \sim 100$~Myrs and the stellar mass in each galaxy grows linearly as a function of time from $z=12$ to $z=5$ (i.e., repeated bursts in each galaxy produce approximately equal mass in stars). The distribution of burst masses across different galaxies follows a power-law $dN/dM_* \propto M_*^α$ with slope $α\sim -2$. At $z>9-10$ the observed galaxy population typically had only one or two bursts of stars formation, hence the observed stellar masses at these redshifts (reaching $M_* \sim 10^{10}$~M$_\odot$), roughly represent the distribution of masses formed in one burst.

Recrystallization is a phenomenon in which a plastically deformed polycrystalline microstructure with a high dislocation density transforms into another that has low dislocation density. This evolution is driven by the stored energy in dislocations, rather than grain growth driven by grain boundary energy alone. One difficulty in quantitative modeling of recrystallization is the uncertainty in material parameters, which can be addressed by integration of experimental data into simulations. In this work, we compare simulated static recrystallization dynamics of a Mg-3Zn-0.1Ca wt.% alloy to experiments involving thermomechanical processing followed by measurements of the recrystallization fraction over time. The simulations are performed by combining PRISMS software for crystal plasticity and phase-field models (PRISMS-Plasticity and PRISMS-PF, respectively) in an integrated computational materials engineering framework. At 20% strain and annealing at 350 °C, the model accurately describes recrystallization dynamics up to a mobility-dependent time scale factor. While the average grain boundary mobility and the fraction of plastic work converted into stored energy are not precisely known, by fitting simulations to experimental data, we show that the average grain boundary mobility can be determined if the fraction of plastic work converted to stored energy is known, or vice versa. For low annealing temperatures, we observe a discrepancy between the model and experiments in the late stages of recrystallization, where a slowdown in recrystallization kinetics occurs in the experiments. We discuss possible sources of this slowdown and propose additional physical mechanisms that need to be accounted for in the model to improve its predictions.

In symmetric private information retrieval (SPIR), a user communicates with multiple servers to retrieve from them a message in a database, while not revealing the message index to any individual server (user privacy), and learning no additional information about the database (database privacy). We study the problem of SPIR on graph-replicated database systems, where each node of the graph represents a server and each link represents a message. Each message is replicated at exactly two servers; those at which the link representing the message is incident. To ensure database privacy, the servers share a set of common randomness, independent of the database and the user's desired message index. We study two cases of common randomness distribution to the servers: i) graph-replicated common randomness, and ii) fully-replicated common randomness. Given a graph-replicated database system, in i), we assign one randomness variable independently to every pair of servers sharing a message, while in ii), we assign an identical set of randomness variable to all servers, irrespective of the underlying graph. In both settings, our goal is to characterize the SPIR capacity, i.e., the maximum number of desired message symbols retrieved per downloaded symbol, and quantify the minimum amount of common randomness required to achieve the capacity. To this goal, in setting i), we derive a general lower bound on the SPIR capacity, and show it to be tight for path and regular graphs through a matching converse. Moreover, we establish that the minimum size of common randomness required for SPIR is equal to the message size. In setting ii), the SPIR capacity improves over the first, more restrictive setting. We show this through capacity lower bounds for a class of graphs, by constructing SPIR schemes from PIR schemes.

The digital services economy consists of online platforms that facilitate interactions between service providers and consumers. This ecosystem is characterized by short-term, often one-off, transactions between parties that have no prior familiarity. To establish trust among users, platforms employ rating systems which allow users to report on the quality of their previous interactions. However, while arguably crucial for these platforms to function, rating systems can perpetuate negative biases against marginalised groups. This paper investigates how to design platforms around biased reputation systems, reducing discrimination while maintaining incentives for all service providers to offer high quality service for users. We introduce an evolutionary game theoretical model to study how digital platforms can perpetuate or counteract rating-based discrimination. We focus on the platforms' decisions to promote service providers who have high reputations or who belong to a specific protected group. Our results demonstrate a fundamental trade-off between user experience and fairness: promoting highly-rated providers benefits users, but lowers the demand for marginalised providers against which the ratings are biased. Our results also provide evidence that intervening by tuning the demographics of the search results is a highly effective way of reducing unfairness while minimally impacting users. Furthermore, we show that even when precise measurements on the level of rating bias affecting marginalised service providers is unavailable, there is still potential to improve upon a recommender system which ignores protected characteristics. Altogether, our model highlights the benefits of proactive anti-discrimination design in systems where ratings are used to promote cooperative behaviour.

We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by the Schrödinger equation on a curved spatial background and, when included, by minimal coupling to a magnetic vector potential incorporating an Aharonov--Bohm flux. After separation of variables, the problem reduces to a one-dimensional radial eigenvalue equation governed by an effective potential that combines torsion-induced Coulomb-like and centrifugal-like structures with magnetic/flux-dependent terms and optional model interactions. Because closed-form analytic solutions are not reliable over the parameter ranges required for systematic scans, we compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem and solving it with a finite-difference discretization on a truncated radial domain, with explicit convergence control. We analyze four representative scenarios: (i) no external potential, (ii) Cornell-type confinement, (iii) Kratzer-type interaction, and (iv) the small-oscillation regime around the minimum of a Morse potential. We present systematic trends of the low-lying levels as functions of the torsion parameter, magnetic field, and azimuthal sector, and we show that geometric couplings alone can produce effective confinement even in the absence of an external interaction.

Thomassen famously proved that every planar graph is 5-choosable. We explore variants of this result, focusing on finding disjoint correspondence colorings, in the more general class of $K_5$-minor-free graphs. Correspondence colorings generalize list colorings as follows. Given a graph $G$ and a positive integer $t$, a correspondence $t$-cover $\textbf{M}$ assigns to each $v\in V(G)$ a set of allowable colors $\{1_v,\ldots,t_v\}$ and to each edge $vw\in E(G)$ a matching between $\{1_v,\ldots,t_v\}$ and $\{1_w,\ldots,t_w\}$. An $\textbf{M}$-coloring $φ$ picks for each vertex $v$ a color $φ(v)$ (from the set $\{1_v,\ldots,t_v\}$) such that for each edge $vw\in E(G)$ the colors $φ(v),φ(w)$ are not matched to each other. Two $\textbf{M}$-colorings $φ_1,φ_2$ of $G$ are called disjoint if $φ_1(v)\neφ_2(v)$ for all $v\in V(G)$. For every $K_5$-minor-free graph $G$ and every correspondence 6-cover $\textbf{M}$ of $G$, we construct 3 pairwise disjoint $\textbf{M}$-colorings $φ_1,φ_2,φ_3$. In contrast, we provide examples of $K_5$-minor-free graphs and correspondence 5-covers $\textbf{M}$ that do not admit 3 disjoint $\textbf{M}$-colorings.

We study scalar waves on subextremal Kerr-de Sitter spacetimes in a compact slow-rotation regime and at a fixed overtone index. Working initially at a fixed cosmological constant $Λ>0$ and uniformly for $(M,a)$ in a compact slow-rotation set, using the meromorphic/Fredholm framework for quasinormal modes and a semiclassical equatorial labeling proved in a companion paper, we establish a quantitative two-mode dominance theorem in an equatorial high-frequency package: after exact azimuthal reduction, microlocal equatorial localization, and analytic pole selection by entire localization weights constructed from equatorial pseudopoles, the $k=\pm\ell$ sector signals are each governed by a single quasinormal exponential, up to an explicitly controlled tail and an $\mathcal O(\ell^{-\infty})$ contribution from all other poles. We then develop a fully deterministic frequency-extraction stability estimate based on time-shift invariance, and combine it with the two-mode dominance result and the companion paper's inverse stability theorem to obtain an explicit parameter bias bound for ringdown-based recovery of $(M,a)$. Finally, using the companion paper's three-parameter inverse theorem and a damping observable based on the scaled imaginary part of one equatorial mode, we propagate the same deterministic error chain to a local bias bound for recovery of $(M,a,Λ)$ on compact parameter sets with $|a|$ bounded away from $0$. As a further consequence, we obtain a localized pseudospectral stability statement for the equatorial resolvent package, quantifying how large microlocalized resolvent norms enforce proximity to the labeled equatorial poles. The resulting estimates clarify the conditioning mechanisms (start time, window length, shift step, and detector nondegeneracy) and provide a rigorous PDE-to-data interface for high-frequency black-hole spectroscopy.

In this article we extend the notion of determinantal representation of hypersurfaces to the determinantal representation of sections of the determinant line bundle of a vector bundle. We give several examples, and prove some necessary conditions for existence of determinantal representation. As an application, we show that for any integer $d \geq 1,$ there is an indecomposable vector bundle $E_d$ of rank $2$ on $\mathbb{P}^2$ such that almost all curves of degree $d$ of $\mathbb{P}^2$ arise as the degeneracy loci of a pair of holomorphic sections of $E_d$, upto an automorphism of $\mathbb{P}^2$. We use this result to obtain a linear algebraic application.

We study the interaction of a kaon with the $f_1(1285)$ resonance, assuming that the $f_1(1285)$ is a molecular state generated by the $K \bar K^*, \bar K K^*$ interaction, evaluating the scattering amplitude, the scattering length and effective range of the $K f_1$ system. The scattering amplitude develops a resonant structure approximately $10$ MeV below the $K f_1$ threshold, with a width of around $15$ MeV. The corresponding correlation function has the distinctive shape of a system with a bound state close to threshold. We also show that the interaction of the $K f_1$ system is differs significantly from the one obtained assuming that the $f_1(1285)$ is an elementary particle. This provides motivation to continue the search for these observables, already initiated by the measurement of the $p f_1(1285)$ correlation function by the ALICE collaboration.

Intermodal quantum key distribution at telecom wavelengths provides a hybrid interface between fiber connections and free-space links, both essential for the realization of scalable and interoperable quantum networks. Although demonstrated over short-range free-space links, long-distance implementations of intermodal quantum key distribution remain challenging, due to turbulence-induced wavefront aberrations which limit efficient single-mode fiber coupling at the optical receiver. Here, we demonstrate a real-time intermodal quantum key distribution field trial over an 18 km free-space link, connecting a remote terminal to an urban optical ground station equipped with a 40 cm-class telescope. An adaptive optics system, implementing direct wavefront sensing and high-order aberration correction, enables efficient single-mode fiber coupling and allows secure key generation of 200 bit/s using a compact state analyzer equipped with room-temperature detectors. We further validate through experimental data a turbulence-based model for predicting fiber coupling efficiency, providing practical design guidelines for future intermodal quantum networks.