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We determine the strong independence number of the qualitative independence hypergraph, $3\text{-}QI(11, 2)$, using a technique that involves considering its vertices as subsets of $\{1,2, \ldots, 11\}$ and assessing them as intersecting set systems. This gives the maximum size of colour classes in any strong colouring and thus, a lower bound on the strong chromatic number of $3\text{-}QI(11,2)$. We leverage this bound along with an upper bound of the strong chromatic number of $3\text{-}QI(10,2)$, to consequently, establish that the covering array number of $3\text{-}QI(11, 2)$, $CAN(3\text{-}QI(11,2),2) = 11$ and give a sufficient condition for a hypergraph $H$ to have $CAN(H, 2)=11$.
While Large Language Models (LLMs) offer a solution to the scale-versus-depth dilemma in qualitative analysis, the paradigm of maximizing automation is fundamentally at odds with the interpretive nature of qualitative inquiry. We argue that effective Human-AI collaboration is not an automation problem, but an interdependence problem. This paper reframes the design of "co-data" systems through the lens of Interdependence Theory, proposing a formal framework to structure human-AI productive interdependence. The framework guides the selection of an appropriate Level of Automation (LoA) for different stages of the qualitative analysis process by assessing task risk and the cost of validation. We present a case study where this framework led to a deliberately interdependent workflow, fostering the calibrated trust necessary for rigorous analysis. We conclude by presenting three design principles that instantiate this framework, demonstrating how to leverage AI as a powerful partner while preserving the human researcher's irreplaceable role in the transformation process of meaning-making.
Qualitative research studies often employ a contextual inquiry, or a field study that involves in-depth observation and interviews of a small sample of study participants, in-situ, to gain a robust understanding of the reasons and circumstances that led to the participant's thoughts, actions, and experiences regarding the domain of interest. Contextual inquiry, especially in sensitive data studies, can be a challenging task due to reasons such as participant privacy, as well as physical constraints such as in-person presence and manual analysis of the qualitative data gathered. In this work, we discuss Enquête Contextuelle Habile Ordinateur (ECHO); a virtual-assistant framework to automate the erstwhile manual process of conducting contextual inquiries and analysing the respondents' subjective qualitative data. ECHO automates the contextual inquiry pipeline, while not compromising on privacy preservation or response integrity. Its adaptive conversational interface enables respondents to provide unstructured or semi-structured responses in free-form natural language, allowing researchers to explore larger narratives in participant response data. It supports response-driven explorato
Recently, large language models have shown great potential to transform online medical consultation. Despite this, most research targets improving diagnostic accuracy with ample information, often overlooking the inquiry phase. Some studies try to evaluate or refine doctor models by using prompt-engineered patient agents. However, prompt engineering alone falls short in accurately simulating real patients. We need to explore new paradigms for patient simulation. Furthermore, the relationship between inquiry and diagnosis remains unexplored. This paper extracts dialogue strategies from real doctor-patient conversations to guide the training of a patient simulator. Our simulator shows higher anthropomorphism and lower hallucination rates, using dynamic dialogue strategies. This innovation offers a more accurate evaluation of diagnostic models and generates realistic synthetic data. We conduct extensive experiments on the relationship between inquiry and diagnosis, showing they adhere to Liebig's law: poor inquiry limits diagnosis effectiveness, regardless of diagnostic skill, and vice versa. The experiments also reveal substantial differences in inquiry performance among models. To d
After major disasters, formal inquiries become arenas where responsibility is publicly contested. While extensive research has examined blame attribution through qualitative and actor-centred approaches, the relational structure of blame within formal accountability processes remains poorly understood. Using evidence from the Grenfell Tower Inquiry, this study analyses the web of blame presented during the Phase 2 closing proceedings, in which Counsel to the Inquiry synthesised how core participants publicly attributed responsibility to one another. We represent this synthesis as a directed network and examine its structural properties using standard tools from network analysis. The resulting configuration is interconnected, with pronounced reciprocity and local clustering, indicating that responsibility claims were articulated within a dense institutional environment rather than as isolated, one-to-one accusations. Comparisons with neutral benchmark models show that several observed features depart from expectations based on simple structural constraints alone, revealing patterned organisation in the public articulation of blame within the Inquiry. By applying network-analytic met
Computational developments--particularly artificial intelligence--are reshaping social scientific research and raise new questions for in-depth methods such as ethnography and qualitative interviewing. Building on classic debates about computers in qualitative data analysis (QDA), we revisit possibilities and dangers in an era of automation, Large Language Model (LLM) chatbots, and 'big data.' We introduce a typology of contemporary approaches to using computers in qualitative research: streamlining workflows, scaling up projects, hybrid analytical methods, the sociology of computation, and technological rejection. Drawing from scaled team ethnographies and solo research integrating computational social science (CSS), we describe methodological choices across study lifecycles, from literature reviews through data collection, coding, text retrieval, and representation. We argue that new technologies hold potential to address longstanding methodological challenges when deployed with knowledge, purpose, and ethical commitment. Yet a pragmatic approach--moving beyond technological optimism and dismissal--is essential given rapidly changing tools that are both generative and dangerous.
We introduce Baichuan-M3, a medical-enhanced large language model engineered to shift the paradigm from passive question-answering to active, clinical-grade decision support. Addressing the limitations of existing systems in open-ended consultations, Baichuan-M3 utilizes a specialized training pipeline to model the systematic workflow of a physician. Key capabilities include: (i) proactive information acquisition to resolve ambiguity; (ii) long-horizon reasoning that unifies scattered evidence into coherent diagnoses; and (iii) adaptive hallucination suppression to ensure factual reliability. Empirical evaluations demonstrate that Baichuan-M3 achieves state-of-the-art results on HealthBench, the newly introduced HealthBench-Hallu and ScanBench, significantly outperforming GPT-5.2 in clinical inquiry, advisory and safety. The models are publicly available at https://huggingface.co/collections/baichuan-inc/baichuan-m3.
Qualitative Spatial Reasoning (QSR) is well explored area of Commonsense Reasoning and has multiple applications ranging from Geographical Information Systems to Robotics and Computer Vision. Recently many claims have been made for the capabilities of Large Language Models (LLMs). In this paper we investigate the extent to which one particular LLM can perform classical qualitative spatial reasoning tasks on the mereotopological calculus, RCC-8.
We present an inquiry lab activity on Circuit Design that was conducted in Fall 2009 with first-year community college students majoring in Electrical Engineering Technology. This inquiry emphasized the use of engineering process skills, including circuit assembly and problem solving, while learning technical content. Content goals of the inquiry emphasized understanding voltage dividers (Kirchoff's voltage law) and analysis and optimization of resistive networks (Thevenin equivalence). We assumed prior exposure to series and parallel circuits and Ohm's law (the relationship between voltage, current, and resistance) and designed the inquiry to develop these skills. The inquiry utilized selection of engineering challenges on a specific circuit (the Wheatstone Bridge) to realize these learning goals. Students generated questions and observations during the starters, which were categorized into four engineering challenges or design goals. The students formed teams and chose one challenge to focus on during the inquiry. We created a rubric for summative assessment which helped to clarify and solidify project goals while designing the inquiry and aided in formative assessment during the
We describe a new inquiry design aimed at teaching advanced high-school to senior college students the basics of stellar populations. The inquiry is designed to have students come up with their own version of the Hertzsprung-Russell diagram as a tool to understand how stars evolve based on their color, mass, and luminosity. The inquiry makes use of pictures and spectra of stars, which the students analyze and interpret to answer the questions they come up with at the beginning. The students undergo a similar experience to real astronomers, using the same tools and methods to figure out the phenomena they are trying to understand. Specifically, they use images and spectra of stars, and organize the data via tables and plots to find trends that will then enable them to answer their questions. The inquiry also includes a "thinking tool" to help connect the trends students observe to the larger picture of stellar evolution. We include a description of the goals of the inquiry, the activity description, the motivations and thoughts that went into the design of the inquiry, and reflections on how the inquiry activity worked in practice.
This article makes two key contributions to methodological debates in automation research. First, we argue for and demonstrate how methods in this field must account for intersections of social difference, such as race, class, ethnicity, culture, and disability, in more nuanced ways. Second, we consider the complexities of bringing together computational and qualitative methods in an intersectional methodological approach while also arguing that in their respective subjects (machines and human subjects) and conceptual scope they enable a specific dialogue on intersectionality and automation to be articulated. We draw on field reflections from a project that combines an analysis of intersectional bias in language models with findings from a community workshop on the frustrations and aspirations produced through engagement with everyday AI-driven technologies in the context of care.
In present paper, with the help of the Faà di Bruno formula and identities of partial Bell polynomials, the author establishes explicit formulas of the Gauss hypergeometric functions \begin{gather*} {\,}_2F_1\biggl(\frac{1-n}{2},\frac{2-n}{2};\frac{3}{2}-m;z^2\biggr), \quad {\,}_2F_1\biggl(-\frac{n}{2},\frac{1-n}{2};\frac{1}{2}-m;z^2\biggr),\\ {\,}_2F_1\biggl(a,a+\frac{1}{2};\frac{3}{2}-m;z^2\biggr), \quad {\,}_2F_1\biggl(a,a+\frac{1}{2};\frac{1}{2}-m;z^2\biggr) \end{gather*} for $m,n\in\mathbb{N}$ and $a\in\mathbb{C}$, and then derives two combinatorial identities \begin{equation*} \sum_{k=0}^{m}\frac{2^k}{k!} \binom{2m-2k}{m-k} \sum_{\ell=0}^{k} \frac{(-1)^\ell}{2^\ell} \frac{(2k-2\ell-1)!!}{(n-\ell)!} \binom{2k-\ell-1}{\ell-1} =\frac{1}{n!}\binom{2m-n}{m} \end{equation*} and \begin{equation*} \sum_{k=1}^{m}\frac{1}{(k!)^2}\binom{2m-2k}{m-k} \sum_{\ell=1}^{k} \binom{k}{\ell}\ell(2k-\ell-1)! (2a)_\ell =\binom{2m+2a}{m}, \end{equation*} where $m\in\mathbb{N}_0$, $n\in\mathbb{Z}$, and $a\in\mathbb{C}$. These newly-established identities generalize the nice and beautiful combinatorial identity \begin{equation*} \sum_{k=0}^{n} \frac{2^{k}}{k!}\binom{2n-2k}{n-k} \sum_{j=0}^{k}\frac{(-1
Clustering can be used to extract insights from data or to verify some of the assumptions held by the domain experts, namely data segmentation. In the literature, few methods can be applied in clustering qualitative values using the context associated with other variables present in the data, without losing interpretability. Moreover, the metrics for calculating dissimilarity between qualitative values often scale poorly for high dimensional mixed datasets. In this study, we propose a novel method for clustering qualitative values, based on Hierarchical Clustering (HQC), and using Maximum Mean Discrepancy. HQC maintains the original interpretability of the qualitative information present in the dataset. We apply HQC to two datasets. Using a mixed dataset provided by Spotify, we showcase how our method can be used for clustering music artists based on the quantitative features of thousands of songs. In addition, using financial features of companies, we cluster company industries, and discuss the implications in investment portfolios diversification.
The rapidly evolving sector of Multi-modal Large Language Models (MLLMs) is at the forefront of integrating linguistic and visual processing in artificial intelligence. This paper presents an in-depth comparative study of two pioneering models: Google's Gemini and OpenAI's GPT-4V(ision). Our study involves a multi-faceted evaluation of both models across key dimensions such as Vision-Language Capability, Interaction with Humans, Temporal Understanding, and assessments in both Intelligence and Emotional Quotients. The core of our analysis delves into the distinct visual comprehension abilities of each model. We conducted a series of structured experiments to evaluate their performance in various industrial application scenarios, offering a comprehensive perspective on their practical utility. We not only involve direct performance comparisons but also include adjustments in prompts and scenarios to ensure a balanced and fair analysis. Our findings illuminate the unique strengths and niches of both models. GPT-4V distinguishes itself with its precision and succinctness in responses, while Gemini excels in providing detailed, expansive answers accompanied by relevant imagery and links
As semiconductor technology nodes scale, computational lithography is essential for ensuring yield and performance. However, lithography is a continuous physical process involving mask optimization, optical imaging, resist exposure, and development, which existing models fail to capture. To overcome this limitation, we present LithoDreamer, the first physics-informed World Model (WM) framework for computational lithography, which formulates the ``Layout-Mask-Resist Image-After Development Image (ADI)'' pipeline as a decision-driven multi-step evolution system. LithoDreamer captures feature changes between adjacent states to model stage-specific physics-informed latent spaces, in which it controls process intervention exploration and drives subsequent state transitions. To achieve interpretable intervention optimization without continuous supervision, we propose a contrastive variational optimization paradigm that contrasts the latent differences between intervention paths with variational evolution constraints, guiding the model to generate evolutions consistent with real lithography physics. Experiments show LithoDreamer achieves state-of-the-art performance in forward evolution a
Despite substantial progress in video understanding, most existing datasets are limited to Earth's gravitational conditions. However, microgravity alters human motion, interactions, and visual semantics, revealing a critical gap for real-world vision systems. This presents a challenge for domain-robust video understanding in safety-critical space applications. To address this, we introduce MicroG-4M, the first benchmark for spatio-temporal and semantic understanding of human activities in microgravity. Constructed from real-world space missions and cinematic simulations, the dataset includes 4,759 clips covering 50 actions, 1,238 context-rich captions, and over 7,000 question-answer pairs on astronaut activities and scene understanding. MicroG-4M supports three core tasks: fine-grained multi-label action recognition, temporal video captioning, and visual question answering, enabling a comprehensive evaluation of both spatial localization and semantic reasoning in microgravity contexts. We establish baselines using state-of-the-art models. All data, annotations, and code are available at https://github.com/LEI-QI-233/HAR-in-Space.
We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation also contains new results, such as optimal estimates (both in terms of stochastic moments and scaling of the error) for coefficient fields which are local functions of Gaussian random fields.
In the note, the authors give a unified proof of Identities~67, 84, and~85 in the monograph "M. Z. Spivey, The Art of Proving Binomial Identities, Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019; available online at https://doi.org/10.1201/9781351215824" and connect these three identities with a computing formula for the Stirling numbers of the second kind. Moreover, in terms of the notion of Qi's normalized remainders of the exponential and logarithmic functions, the authors reformulate the definitions of the Stirling numbers of the first and second kind and their generalizations by Howard in 1967 and 1980, Carlitz in 1980, and Broder in 1984.
In this paper, we study the Chevalley property of Cayley-Hamilton Hopf algebras in the sense of De Concini-Procesi-Reshetikhin-Rosso using discriminant ideals. For any affine Cayley-Hamilton Hopf algebra $(H,C,\text{tr})$ whose identity fiber algebra has the Chevalley property, we prove that an irreducible $H$-module $V$ has the property that $V\otimes W$ is a completely reducible $H$-module for every irreducible $H$-module $W$ if and only if $V$ is annihilated by the lowest discriminant ideal of $(H,C,\text{tr})$, which establishes a bridge between the tensor-nondegenerate behaviour of the irreducible representations of $H$ and the lowest discriminant ideal of $(H,C,\text{tr})$. Using discriminant ideals, we prove that an affine Cayley-Hamilton Hopf algebra $(H,C,\text{tr})$ has the Chevalley property if and only if its identity fiber algebra $H/\mathfrak{m}_{\overline{\varepsilon}}H$ has the Chevalley property and all the discriminant ideals of $(H,C,\text{tr})$ are trivial, thereby resolving a question posed by Huang-Mi-Qi-Wu. Moreover, it is shown that the lowest discriminant subvariety $\mathcal{V}_{\ell}$ of the algebraic group $\operatorname{maxSpec}C$ is a closed subgroup,
Most existing 3D Gaussian Splatting (3DGS) compression schemes focus on producing compact 3DGS representation via implicit data embedding. They have long coding times and highly customized data format, making it difficult for widespread deployment. This paper presents a new 3DGS compression framework called HybridGS, which takes advantage of both compact generation and standardized point cloud data encoding. HybridGS first generates compact and explicit 3DGS data. A dual-channel sparse representation is introduced to supervise the primitive position and feature bit depth. It then utilizes a canonical point cloud encoder to perform further data compression and form standard output bitstreams. A simple and effective rate control scheme is proposed to pivot the interpretable data compression scheme. At the current stage, HybridGS does not include any modules aimed at improving 3DGS quality during generation. But experiment results show that it still provides comparable reconstruction performance against state-of-the-art methods, with evidently higher encoding and decoding speed. The code is publicly available at https://github.com/Qi-Yangsjtu/HybridGS.