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Let $k$ and $n$ be natural numbers. Let $\omega_k(n)$ denote the number of distinct prime factors of $n$ with multiplicity $k$ as studied by Elma and the third author. We obtain asymptotic estimates for the first and the second moments of $\omega_k(n)$ when restricted to the set of $h$-free and $h$-full numbers. We prove that $\omega_1(n)$ has normal order $\log \log n$ over $h$-free numbers, $\omega_h(n)$ has normal order $\log \log n$ over $h$-full numbers, and both of them satisfy the Erd\H{o}s-Kac Theorem. Finally, we prove that the functions $\omega_k(n)$ with $1 < k < h$ do not have normal order over $h$-free numbers and $\omega_k(n)$ with $k > h$ do not have normal order over $h$-full numbers., Comment: To appear in the Journal of Number Theory, 26 pages. arXiv admin note: text overlap with arXiv:2409.10430

Let $\omega(n)$ denote the number of distinct prime factors of a natural number $n$. In 1917, Hardy and Ramanujan proved that $\omega(n)$ has normal order $\log \log n$ over naturals. In this work, we establish the first and the second moments of $\omega(n)$ over $h$-free and $h$-full numbers using a new counting argument and prove that $\omega(n)$ has normal order $\log \log n$ over these subsets., Comment: 23 pages

Let $k \geq 1$ be a natural number and $f \in \mathbb{F}_q[t]$ be a monic polynomial. Let $\omega_k(f)$ denote the number of distinct monic irreducible factors of $f$ with multiplicity $k$. We obtain asymptotic estimates for the first and the second moments of $\omega_k(f)$ with $k \geq 1$. Moreover, we prove that the function $\omega_1(f)$ has normal order $\log (\text{deg}(f))$ and also satisfies the Erd\H{o}s-Kac Theorem. Finally, we prove that the functions $\omega_k(f)$ with $k \geq 2$ do not have normal order.

Recommender systems have become integral to digital experiences, shaping user interactions and preferences across various platforms. Despite their widespread use, these systems often suffer from algorithmic biases that can lead to unfair and unsatisfactory user experiences. This study introduces an interactive tool designed to help users comprehend and explore the impacts of algorithmic harms in recommender systems. By leveraging visualizations, counterfactual explanations, and interactive modules, the tool allows users to investigate how biases such as miscalibration, stereotypes, and filter bubbles affect their recommendations. Informed by in-depth user interviews, this tool benefits both general users and researchers by increasing transparency and offering personalized impact assessments, ultimately fostering a better understanding of algorithmic biases and contributing to more equitable recommendation outcomes. This work provides valuable insights for future research and practical applications in mitigating bias and enhancing fairness in machine learning algorithms.

Elected officials have privileged roles in public communication. In contrast to national politicians, whose posting content is more likely to be closely scrutinized by a robust ecosystem of nationally focused media outlets, sub-national politicians are more likely to openly disseminate harmful content with limited media scrutiny. In this paper, we analyze the factors that explain the online visibility of over 6.5K unique state legislators in the US and how their visibility might be impacted by posting low-credibility or uncivil content. We conducted a study of posting on Twitter and Facebook (FB) during 2020-21 to analyze how legislators engage with users on these platforms. The results indicate that distributing content with low-credibility information attracts greater attention from users on FB and Twitter for Republicans. Conversely, posting content that is considered uncivil on Twitter receives less attention. A noticeable scarcity of posts containing uncivil content was observed on FB, which may be attributed to the different communication patterns of legislators on these platforms. In most cases, the effect is more pronounced among the most ideologically extreme legislators. Our research explores the influence exerted by state legislators on online political conversations, with Twitter and FB serving as case studies. Furthermore, it sheds light on the differences in the conduct of political actors on these platforms. This study contributes to a better understanding of the role that political figures play in shaping online political discourse., Comment: Accepted for publication in the International AAAI Conference on Web and Social Media (ICWSM) 2025

Online discussions frequently involve conspiracy theories, which can contribute to the proliferation of belief in them. However, not all discussions surrounding conspiracy theories promote them, as some are intended to debunk them. Existing research has relied on simple proxies or focused on a constrained set of signals to identify conspiracy theories, which limits our understanding of conspiratorial discussions across different topics and online communities. This work establishes a general scheme for classifying discussions related to conspiracy theories based on authors' perspectives on the conspiracy belief, which can be expressed explicitly through narrative elements, such as the agent, action, or objective, or implicitly through references to known theories, such as chemtrails or the New World Order. We leverage human-labeled ground truth to train a BERT-based model for classifying online CTs, which we then compared to the Generative Pre-trained Transformer machine (GPT) for detecting online conspiratorial content. Despite GPT's known strengths in its expressiveness and contextual understanding, our study revealed significant flaws in its logical reasoning, while also demonstrating comparable strengths from our classifiers. We present the first large-scale classification study using posts from the most active conspiracy-related Reddit forums and find that only one-third of the posts are classified as positive. This research sheds light on the potential applications of large language models in tasks demanding nuanced contextual comprehension., Comment: 12 pages, 6 tables, 1 figure, conference ICWSM_24

Language models demonstrate fundamental abilities in syntax, semantics, and reasoning, though their performance often depends significantly on the inputs they process. This study introduces TSIS (Simplified TSID) and its variants:TSISD (TSIS with Depth-First Search), TSISO (TSIS in Order), and TSISR (TSIS in Random), as integral components of the t-SMILES framework. These additions complete the framework's design, providing diverse approaches to molecular representation. Through comprehensive analysis and experiments employing deep generative models, including GPT, diffusion models, and reinforcement learning, the findings reveal that the hierarchical structure of t-SMILES is more straightforward to parse than initially anticipated. Furthermore, t-SMILES consistently outperforms other linear representations such as SMILES, SELFIES, and SAFE, demonstrating superior convergence speed and enhanced generalization capabilities., Comment: 26pages, 6 figures

Despite the benefits of personalizing items and information tailored to users' needs, it has been found that recommender systems tend to introduce biases that favor popular items or certain categories of items, and dominant user groups. In this study, we aim to characterize the systematic errors of a recommendation system and how they manifest in various accountability issues, such as stereotypes, biases, and miscalibration. We propose a unified framework that distinguishes the sources of prediction errors into a set of key measures that quantify the various types of system-induced effects, both at the individual and collective levels. Based on our measuring framework, we examine the most widely adopted algorithms in the context of movie recommendation. Our research reveals three important findings: (1) Differences between algorithms: recommendations generated by simpler algorithms tend to be more stereotypical but less biased than those generated by more complex algorithms. (2) Disparate impact on groups and individuals: system-induced biases and stereotypes have a disproportionate effect on atypical users and minority groups (e.g., women and older users). (3) Mitigation opportunity: using structural equation modeling, we identify the interactions between user characteristics (typicality and diversity), system-induced effects, and miscalibration. We further investigate the possibility of mitigating system-induced effects by oversampling underrepresented groups and individuals, which was found to be effective in reducing stereotypes and improving recommendation quality. Our research is the first systematic examination of not only system-induced effects and miscalibration but also the stereotyping issue in recommender systems.

This survey study focuses on public opinion regarding the use of algorithmic decision-making in government sectors, specifically in Allegheny County, Pennsylvania. Algorithms are becoming increasingly prevalent in various public domains, including both routine and high-stakes government functions. Despite their growing use, public sentiment remains divided, with concerns about privacy and accuracy juxtaposed against perceptions of fairness when compared to human decision-making. In April 2021, a survey was conducted among nearly 1,500 county residents to explore their awareness, experiences, and attitudes towards these algorithms. The study highlights diverse viewpoints influenced by factors such as race, age, education, gender, income, and urban or suburban living. The results demonstrate the complexity of public sentiment towards algorithmic governance and emphasize the need for a nuanced understanding and approach in policy and implementation.

The escalating food insecurity in Africa, caused by factors such as war, climate change, and poverty, demonstrates the critical need for advanced early warning systems. Traditional methodologies, relying on expert-curated data encompassing climate, geography, and social disturbances, often fall short due to data limitations, hindering comprehensive analysis and potential discovery of new predictive factors. To address this, this paper introduces "HungerGist", a multi-task deep learning model utilizing news texts and NLP techniques. Using a corpus of over 53,000 news articles from nine African countries over four years, we demonstrate that our model, trained solely on news data, outperforms the baseline method trained on both traditional risk factors and human-curated keywords. In addition, our method has the ability to detect critical texts that contain interpretable signals known as "gists." Moreover, our examination of these gists indicates that this approach has the potential to reveal latent factors that would otherwise remain concealed in unstructured texts.

Big data and machine learning tools have jointly empowered humans in making data-driven decisions. However, many of them capture empirical associations that might be spurious due to confounding factors and subgroup heterogeneity. The famous Simpson's paradox is such a phenomenon where aggregated and subgroup-level associations contradict with each other, causing cognitive confusions and difficulty in making adequate interpretations and decisions. Existing tools provide little insights for humans to locate, reason about, and prevent pitfalls of spurious association in practice. We propose VISPUR, a visual analytic system that provides a causal analysis framework and a human-centric workflow for tackling spurious associations. These include a CONFOUNDER DASHBOARD, which can automatically identify possible confounding factors, and a SUBGROUP VIEWER, which allows for the visualization and comparison of diverse subgroup patterns that likely or potentially result in a misinterpretation of causality. Additionally, we propose a REASONING STORYBOARD, which uses a flow-based approach to illustrate paradoxical phenomena, as well as an interactive DECISION DIAGNOSIS panel that helps ensure accountable decision-making. Through an expert interview and a controlled user experiment, our qualitative and quantitative results demonstrate that the proposed "de-paradox" workflow and the designed visual analytic system are effective in helping human users to identify and understand spurious associations, as well as to make accountable causal decisions.

The Russian invasion of Ukraine has elicited a diverse array of responses from nations around the globe. During a global conflict, polarized narratives are spread on social media to sway public opinion. We examine the dynamics of the political narratives surrounding the Russia-Ukraine war during the first two months of the Russian invasion of Ukraine (RU) using the Chinese Twitter space as a case study. Since the beginning of the RU, pro-Chinese-state and anti-Chinese-state users have spread divisive opinions, rumors, and conspiracy theories. We investigate how the pro- and anti-state camps contributed to the evolution of RU-related narratives, as well as how a few influential accounts drove the narrative evolution. We identify pro-state and anti-state actors on Twitter using network analysis and text-based classifiers, and we leverage text analysis, along with the users' social interactions (e.g., retweeting), to extract narrative coordination and evolution. We find evidence that both pro-state and anti-state camps spread propaganda narratives about RU. Our analysis illuminates how actors coordinate to advance particular viewpoints or act against one another in the context of global conflict., Comment: To be published in International Conference on Social Computing, Behavioral-Cultural Modeling, & Prediction and Behavior Representation in Modeling and Simulation (SBP-BRiMS), 2023

In-time particle trajectory reconstruction in the Large Hadron Collider is challenging due to the high collision rate and numerous particle hits. Using GNN (Graph Neural Network) on FPGA has enabled superior accuracy with flexible trajectory classification. However, existing GNN architectures have inefficient resource usage and insufficient parallelism for edge classification. This paper introduces a resource-efficient GNN architecture on FPGAs for low latency particle tracking. The modular architecture facilitates design scalability to support large graphs. Leveraging the geometric properties of hit detectors further reduces graph complexity and resource usage. Our results on Xilinx UltraScale+ VU9P demonstrate 1625x and 1574x performance improvement over CPU and GPU respectively.

Literacy is one of the most fundamental skills for people to access and navigate today's digital environment. This work systematically studies the language literacy skills of online populations for more than 160 countries and regions across the world, including many low-resourced countries where official literacy data are particularly sparse. Leveraging public data on Facebook, we develop a population-level literacy estimate for the online population that is based on aggregated and de-identified public posts written by adult Facebook users globally, significantly improving both the coverage and resolution of existing literacy tracking data. We found that, on Facebook, women collectively show higher language literacy than men in many countries, but substantial gaps remain in Africa and Asia. Further, our analysis reveals a considerable regional gap within a country that is associated with multiple socio-technical inequalities, suggesting an "inequality paradox" -- where the online language skill disparity interacts with offline socioeconomic inequalities in complex ways. These findings have implications for global women's empowerment and socioeconomic inequalities.

With the rise of AI and data mining techniques, group profiling and group-level analysis have been increasingly used in many domains including policy making and direct marketing. In some cases, the statistics extracted from data may provide insights to a group's shared characteristics; in others, the group-level analysis can lead to problems including stereotyping and systematic oppression. How can analytic tools facilitate a more conscientious process in group analysis? In this work, we identify a set of accountable group analytics design guidelines to explicate the needs for group differentiation and preventing overgeneralization of a group. Following the design guidelines, we develop TribalGram, a visual analytic suite that leverages interpretable machine learning algorithms and visualization to offer inference assessment, model explanation, data corroboration, and sense-making. Through the interviews with domain experts, we showcase how our design and tools can bring a richer understanding of "groups" mined from the data.

Classification models learn to generalize the associations between data samples and their target classes. However, researchers have increasingly observed that machine learning practice easily leads to systematic errors in AI applications, a phenomenon referred to as AI blindspots. Such blindspots arise when a model is trained with training samples (e.g., cat/dog classification) where important patterns (e.g., black cats) are missing or periphery/undesirable patterns (e.g., dogs with grass background) are misleading towards a certain class. Even more sophisticated techniques cannot guarantee to capture, reason about, and prevent the spurious associations. In this work, we propose ESCAPE, a visual analytic system that promotes a human-in-the-loop workflow for countering systematic errors. By allowing human users to easily inspect spurious associations, the system facilitates users to spontaneously recognize concepts associated misclassifications and evaluate mitigation strategies that can reduce biased associations. We also propose two statistical approaches, relative concept association to better quantify the associations between a concept and instances, and debias method to mitigate spurious associations. We demonstrate the utility of our proposed ESCAPE system and statistical measures through extensive evaluation including quantitative experiments, usage scenarios, expert interviews, and controlled user experiments.

White supremacist extremist groups are a significant domestic terror threat in many Western nations. These groups harness the Internet to spread their ideology via online platforms: blogs, chat rooms, forums, and social media, which can inspire violence offline. In this work, we study the persistence and reach of white supremacist propaganda in both online and offline environments. We also study patterns in narratives that crossover from online to offline environments, or vice versa. From a geospatial analysis, we find that offline propaganda is geographically widespread in the United States, with a slight tendency toward Northeastern states. Propaganda that spreads the farthest and lasts the longest has a patriotic framing and is short, memorable, and repeatable. Through text comparison methods, we illustrate that online propaganda typically leads the appearance of the same propaganda in offline flyers, banners, and graffiti. We hope that this study sheds light on the characteristics of persistent white supremacist narratives both online and offline., Comment: 9 pages, 6 figures, Companion Proceedings of the ACM Web Conference 2023 (WWW '23 Companion), April 30-May 4, 2023, Austin, TX, USA

Effective representation of molecules is a crucial factor affecting the performance of artificial intelligence models. This study introduces a flexible, fragment-based, multiscale molecular representation framework called t-SMILES (tree-based SMILES) with three code algorithms: TSSA, TSDY and TSID. It describes molecules using SMILES-type strings obtained by performing a breadth-first search on a full binary tree formed from a fragmented molecular graph. Systematic evaluations using JTVAE, BRICS, MMPA, and Scaffold show the feasibility of constructing a multi-code molecular description system, where various descriptions complement each other, enhancing the overall performance. In addition, it can avoid overfitting and achieve higher novelty scores while maintaining reasonable similarity on labeled low-resource datasets, regardless of whether the model is original, data-augmented, or pre-trained then fine-tuned. Furthermore, it significantly outperforms classical SMILES, DeepSMILES, SELFIES and baseline models in goal-directed tasks. And it surpasses state-of-the-art fragment, graph and SMILES based approaches on ChEMBL, Zinc, and QM9.