Single-cell RNA-seq data analysis typically requires representations that capture heterogeneous local structure across multiple scales while remaining stable and interpretable. In this work, we propose a hierarchical sheaf spectral embedding (HSSE) framework that constructs informative cell-level features based on persistent sheaf Laplacian analysis. Starting from scale-dependent low-dimensional embeddings, we define cell-centered local neighborhoods at multiple resolutions. For each local neighborhood, we construct a data-driven cellular sheaf that encodes local relationships among cells. We then compute persistent sheaf Laplacians over sampled filtration intervals and extract spectral statistics that summarize the evolution of local relational structure across scales. These spectral descriptors are aggregated into a unified feature vector for each cell and can be directly used in downstream learning tasks without additional model training. We evaluate HSSE on twelve benchmark single-cell RNA-seq datasets covering diverse biological systems and data scales. Under a consistent classification protocol, HSSE achieves competitive or improved performance compared with existing multiscale and classical embedding-based methods across multiple evaluation metrics. The results demonstrate that sheaf spectral representations provide a robust and interpretable approach for single-cell RNA-seq data representation learning.

A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal trajectory as a parameter-dependent polynomial system for the control switching sequence. A deflated Newton's method is then applied to exhaust all the real roots of the polynomial system. The root-finding procedure is informed by the Hermite quadratic form, which provides a sharp estimate on the number of real roots to be found. In the second part of the paper, the polynomial systems are sampled and solved to generate a synthetic dataset for the construction of a time-optimal deep neural network -- interpreted as a binary classifier -- via supervised learning. Numerical tests in integrators of increasing dimension assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.

Deception is a common strategy adapted by autonomous systems in adversarial settings. Existing deception methods primarily focus on increasing opacity or misdirecting agents away from their goal or itinerary. In this work, we propose a deception problem aiming to mislead the robot towards a decoy goal through altering sensor events under a constrained budget of alteration. The environment along with the robot's interaction with it is modeled as a Partially Observable Markov Decision Process (POMDP), and the robot's action selection is governed by a Finite State Controller (FSC). Given a constrained budget for sensor event modifications, the objective is to compute a sensor alteration that maximizes the probability of the robot reaching a decoy goal. We establish the computational hardness of the problem by a reduction from the $0/1$ Knapsack problem and propose a Mixed Integer Linear Programming (MILP) formulation to compute optimal deception strategies. We show the efficacy of our MILP formulation via a sequence of experiments.

Clinician notes are a rich source of patient information but often contain inconsistencies due to varied writing styles, colloquialisms, abbreviations, medical jargon, grammatical errors, and non-standard formatting. These inconsistencies hinder the extraction of meaningful data from electronic health records (EHRs), posing challenges for quality improvement, population health, precision medicine, decision support, and research. We present a large language model approach to standardizing a corpus of 1,618 clinical notes. Standardization corrected an average of $4.9 +/- 1.8$ grammatical errors, $3.3 +/- 5.2$ spelling errors, converted $3.1 +/- 3.0$ non-standard terms to standard terminology, and expanded $15.8 +/- 9.1$ abbreviations and acronyms per note. Additionally, notes were re-organized into canonical sections with standardized headings. This process prepared notes for key concept extraction, mapping to medical ontologies, and conversion to interoperable data formats such as FHIR. Expert review of randomly sampled notes found no significant data loss after standardization. This proof-of-concept study demonstrates that standardization of clinical notes can improve their readability, consistency, and usability, while also facilitating their conversion into interoperable data formats.

Radio remains a pervasive medium for mass information dissemination, with AM/FM stations reaching more Americans than either smartphone-based social networking or live television. Increasingly, radio broadcasts are also streamed online and accessed over the Internet. We present WavePulse, a framework that records, documents, and analyzes radio content in real-time. While our framework is generally applicable, we showcase the efficacy of WavePulse in a collaborative project with a team of political scientists focusing on the 2024 Presidential Elections. We use WavePulse to monitor livestreams of 396 news radio stations over a period of three months, processing close to 500,000 hours of audio streams. These streams were converted into time-stamped, diarized transcripts and analyzed to track answer key political science questions at both the national and state levels. Our analysis revealed how local issues interacted with national trends, providing insights into information flow. Our results demonstrate WavePulse's efficacy in capturing and analyzing content from radio livestreams sourced from the Web. Code and dataset can be accessed at \url{https://wave-pulse.io}.

The surge of data available on the internet has led to the adoption of various computational methods to analyze and extract valuable insights from this wealth of information. Among these, the field of Machine Learning (ML) has thrived by leveraging data to extract meaningful insights. However, ML techniques face notable challenges when dealing with real-world data, often due to issues of imbalance, noise, insufficient labeling, and high dimensionality. To address these limitations, some researchers advocate for the adoption of Topological Data Analysis (TDA), a statistical approach that discerningly captures the intrinsic shape of data despite noise. Despite its potential, TDA has not gained as much traction within the Natural Language Processing (NLP) domain compared to structurally distinct areas like computer vision. Nevertheless, a dedicated community of researchers has been exploring the application of TDA in NLP, yielding 87 papers we comprehensively survey in this paper. Our findings categorize these efforts into theoretical and non-theoretical approaches. Theoretical approaches aim to explain linguistic phenomena from a topological viewpoint, while non-theoretical approaches merge TDA with ML features, utilizing diverse numerical representation techniques. We conclude by exploring the challenges and unresolved questions that persist in this niche field. Resources and a list of papers on this topic can be found at: https://github.com/AdaUchendu/AwesomeTDA4NLP.

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals. Most of the previous topological signal processing algorithms treat node and edge signals separately and work under the hypothesis that the true signal is smooth and/or well approximated by a harmonic eigenvector of the Hodge-Laplacian, which may be violated in practice. Here we propose Dirac-equation signal processing, a framework for efficiently reconstructing true signals on nodes and edges, also if they are not smooth or harmonic, by processing them jointly. The proposed physics-inspired algorithm is based on the spectral properties of the topological Dirac operator. It leverages the mathematical structure of the topological Dirac equation to boost the performance of the signal processing algorithm. We discuss how the relativistic dispersion relation obeyed by the topological Dirac equation can be used to assess the quality of the signal reconstruction. Finally, we demonstrate the improved performance of the algorithm with respect to previous algorithms. Specifically, we show that Dirac-equation signal processing can also be used efficiently if the true signal is a non-trivial linear combination of more than one eigenstate of the Dirac equation, as it generally occurs for real signals.

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion -- the time-dependent Schr\"odinger equation (TDSE) -- is numerically intractable. We present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

Suicide is a critical global health problem involving more than 700,000 deaths yearly, particularly among young adults. Many people express their suicidal thoughts on social media platforms such as Reddit. This paper evaluates the effectiveness of the deep learning transformer-based models BERT, RoBERTa, DistilBERT, ALBERT, and ELECTRA and various Long Short-Term Memory (LSTM) based models in detecting suicidal ideation from user posts on Reddit. Toward this objective, we curated an extensive dataset from diverse subreddits and conducted linguistic, topic modeling, and statistical analyses to ensure data quality. Our results indicate that each model could reach high accuracy and F1 scores, but among them, RoBERTa emerged as the most effective model with an accuracy of 93.22% and F1 score of 93.14%. An LSTM model that uses attention and BERT embeddings performed as the second best, with an accuracy of 92.65% and an F1 score of 92.69%. Our findings show that transformer-based models have the potential to improve suicide ideation detection, thereby providing a path to develop robust mental health monitoring tools from social media. This research, therefore, underlines the undeniable prospect of advanced techniques in Natural Language Processing (NLP) while improving suicide prevention efforts.

Large Language Models (LLMs) are increasingly used in everyday life and research. One of the most common use cases is conversational interactions, enabled by the language generation capabilities of LLMs. Just as between two humans, a conversation between an LLM-powered entity and a human depends on the personality of the conversants. However, measuring the personality of a given LLM is currently a challenge. This paper introduces the Language Model Linguistic Personality Assessment (LMLPA), a system designed to evaluate the linguistic personalities of LLMs. Our system helps to understand LLMs' language generation capabilities by quantitatively assessing the distinct personality traits reflected in their linguistic outputs. Unlike traditional human-centric psychometrics, the LMLPA adapts a personality assessment questionnaire, specifically the Big Five Inventory, to align with the operational capabilities of LLMs, and also incorporates the findings from previous language-based personality measurement literature. To mitigate sensitivity to the order of options, our questionnaire is designed to be open-ended, resulting in textual answers. Thus, the AI rater is needed to transform ambiguous personality information from text responses into clear numerical indicators of personality traits. Utilising Principal Component Analysis and reliability validations, our findings demonstrate that LLMs possess distinct personality traits that can be effectively quantified by the LMLPA. This research contributes to Human-Computer Interaction and Human-Centered AI, providing a robust framework for future studies to refine AI personality assessments and expand their applications in multiple areas, including education and manufacturing.