arXiv preprints from January 1, 2026 through September 7, 2026 — 09:21:59 EST
Markov chain pool decoding (MCPD) devised by Knill et al. (1996) identifies likely positive clones from noisy pooled-test results. The standard MCPD estimates clone-wise posterior probabilities using Gibbs sampling, but it may allocate excessive computational effort to low-scoring clones. This paper focuses on parallelizing MCPD on...
We propose a new design of fair classifiers for multi-class classification problems in the presence of vector-valued sensitive attributes. In that scenario each sensitive attribute has multiple values and forms several groups relevant to the fairness consideration. Naturally those groups are overlapping and one should also analyze the...
Studies with staggered entry, in which individuals enroll at different calendar times, are ubiquitous in medicine and related disciplines. Because these studies usually have a fixed administrative end of follow-up, identification of the estimand of interest relies on assumptions about the right-censoring mechanism. The assumptions are...
We develop a multifidelity method for fusing low-resolution simulations with computationally expensive high-resolution simulations, which are run infrequently and are therefore prone to bias. We formulate this fusion as a constrained optimization under missing-not-at-random (MNAR) selection bias. This formulation searches for the...
We introduce a robust clustering method, MK-means DPD, that estimates cluster centers and covariance matrices using density power divergence (DPD) measures combined with Mahalanobis distance, making it resistant to outliers and adaptable to heterogeneous, elliptical clusters, unlike the classical K-means algorithm. Since Mahalanobis...
Token prediction is a central pre-training objective for modern language models. Despite its empirical success, why token prediction learns broadly useful representations remains incompletely understood. We develop a statistical framework connecting token prediction with representation geometry, encoder approximation, and downstream...
Missing data, measurement error, and population heterogeneity are pervasive challenges in analyzing data arising from modern observational studies and machine learning applications. Although these problems frequently coexist and interact, they are often treated separately in existing works. We propose a unified probabilistic framework...
Integrals of spectral densities are frequently used to summarize spectral characteristics of linear processes. This work studies self-normalization for estimators of such integrals based on sequential periodograms and establishes weak convergence of the corresponding processes. For linear functionals of the spectral density,...
Introduction: Longitudinal lung function recovery after pulmonary disease commonly follows nonlinear trajectories, and failure to adequately model these trajectories can lead to biased or misleading estimates of treatment effects. However, an important methodological gap remains as there is limited assessment of statistical methods...
Compositional data are positive multivariate data whose sum equals 1. A popular method to analyze such data is via log--ratio transformations, which are however not applicable when zero values are present. In this paper we present a conditional logistic normal distribution suitable for compositional data with structural zero values....
Via Computational Taxonomy (CT), we develop Design of Experiment(DoE) based on rigorously redefined constituting ingredients of complex system dynamics: randomness, nonlinearity and even class, through a data-driven constructed Taxonomic Hierarchy. As an opposite quest of Classification without man-made assumptions and structures, we...
Multilinear principal component analysis (MPCA) reduces the dimension of tensor-valued data while preserving their mode-specific structure, but its quadratic scatter criterion can be unstable under heavy-tailed distributions and contamination. We propose spatial-sign-based multilinear principal component analysis (SMPCA), a robust...
Win statistics require a prespecified outcome hierarchy. Clinical teams sometimes agree only on the highest priority outcome, leaving the order of lower priority outcomes unresolved, and clinically meaningful thresholds may be specified as ranges. Separate sensitivity analyses describe how the results change. A single inference for...
We derive the complete duality theory underlying the Hodrick--Prescott filter, whose rank-deficient second-difference penalty admits infinitely many equivalent trend representations via generalized inverses. Constructing two canonical choices---the Moore--Penrose-based \emph{B-representation} and an alternative...
Renewables now dominate Great Britain's generation mix but rarely occupy the marginal price-setting position, which raises the question of which flexible technologies translate a renewable-rich system into real-time price formation. This study reconstructs the price-ranked edge of the eligible bid or offer stack in the GB Balancing...
Understanding why a target metric changes is a fundamental problem in data-driven decision making, beyond anomaly detection alone. We study root cause attribution for metric changes in complex e-commerce systems, focusing on trade-offs between interpretability, efficiency, and causal validity. As a starting point, we extend a...
Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But...
We consider the Boolean function ${\rm SMul}_{n-1}^n(\boldsymbol{x},\boldsymbol{y})$, which computes the middle bit of the multiplication of two natural numbers represented as $n$-bit binary strings $\boldsymbol{x}$ and $\boldsymbol{y}$, drawn from a restricted domain. We investigate the width of OBDDs computing ${\rm SMul}_{n-1}^n$....
Wireless-enabled physical artificial intelligence (physical AI) systems call for a shift from reliable data delivery to reliable inference of physical events. The relevant question is not only whether packets arrive, but whether the set of cues available at the decision node, i.e., the evidence, is sufficiently timely and informative...
This paper presents Murano, an open source framework for designing, running, and reproducing mechanistic interpretability studies of large language models, intended for researchers across disciplines. These studies often combine loading, recording, attribution, intervention, and evaluation, while existing libraries tend to focus on...
Large language model-based multi-agent systems are evolving from fixed interaction topologies toward dynamically orchestrated Agent Swarms. However, existing benchmarks are still largely based on single-agent or general-purpose agent tasks, making it difficult to systematically evaluate key orchestration capabilities. We propose...
Quantum cooling is important for reliable quantum computation but involves a trade-off between cooling performance and implementation resources. Although reservoir memory can improve particular aspects of cooling performance, the associated resource cost, particularly for circuit implementation, remains insufficiently understood....
Large language models (LLMs) are increasingly used in software development, but their use in complex hardware design remains limited. This gap stems from both the scarcity of public hardware training data and the fundamentally different methodologies used in hardware design. In particular, applying LLMs to hardware requires more than...
We study higher regularity and its relation to nonresonant behavior for time-periodic solutions of boundary value problems for one-dimensional linear and nonlinear nonautonomous first-order integro-differential strictly hyperbolic systems. The boundary conditions include integral operators and various types of boundary reflections. We...
Fixed-viewpoint infrastructure sensors repeatedly observe the same traffic space, making roadside 3D occupancy structurally different from ego-vehicle perception: a near-persistent static scaffold is overlaid with sparse, short-lived dynamic events. Existing occupancy benchmarks and methods, however, are built around moving ego...