Physical Sciences and Mathematics Commons^™

Ai, Medicine, And Social Determinants Of Health Data, Ryan Doyloo, Nicholson Price

Articles

This article examines how medical AI systems are incorporating SDoH data and the governance challenges that follow. The authors show that while SDoH integration can enhance clinical workflows and predictive accuracy — potentially improving outcomes for underserved populations — it also introduces acute risks of proxy discrimination, where facially neutral variables replicate protected characteristics. Surveying U.S., EU, and international frameworks, the authors argue that existing regimes lack clear ex ante guidance to distinguish beneficial from harmful uses of SDoH data. In response, they advance post-market monitoring as a pragmatic and scalable pathway: generating real-world, SDoH-stratified evidence that can support enforcement, …

Saturated Hierarchical Atomic Incremental Learning (Shail): A Behavioral Learning Perspective On Staged Mastery And Saturation, Ernest Fokoue

Articles

We introduce Saturated Hierarchical Atomic Incremental Learning (sHAIL), a learning paradigm in which complex tasks are approached through a sequence of simpler atomic subtasks, each mastered to saturation before progression. The central mechanism is a saturation criterion that detects when learning dynamics enter a plateau region, triggering consolidation and subsequent ascent to a higher level of task complexity. We develop a theoretical framework for sHAIL and show that it naturally gives rise to \emph{staircased convergence}: alternating phases of rapid improvement and genuine plateau. Within each level, classical convergence guarantees apply under standard smoothness conditions, while the hierarchical transitions are driven …

No Intelligence Without Statistics: The Invisible Backbone Of Artificial Intelligence, Ernest Fokoue

Articles

The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars—Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification—demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the …

Decorrelation, Diversity, And Emergent Intelligence: The Isomorphism Between Social Insect Colonies And Ensemble Machine Learning, Ernest Fokoue, Gregory Babbitt, Yuval Levental

Articles

Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation— through stochastic response to local cues and positive feedback—map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that …

A General Weighting Theory For Ensemble Learning: Beyond Variance Reduction Via Spectral And Geometric Structure, Ernest Fokoue

Articles

Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines, kernel ridge regression, Gaussian process regression, and other regularized reproducing kernel Hilbert space (RKHS) methods whose variance is already tightly controlled by regularization and spectral shrinkage. This paper develops a general weighting theory for ensemble learning that moves beyond classical variance-reduction arguments. We formalize ensembles as linear operators acting on a hypothesis space and endow the space of weighting sequences with geometric and spectral constraints. …

On The Scientific Stature Of Data Science: The Epistemological Unicorn, Ernest Fokoue

Articles

Data Science has ignited unprecedented academic, industrial, and pedagogical fervor, yet its status as a \textit{science} in the classical sense---comparable to physics or biology---remains profoundly unsettled. This article interrogates the epistemological foundations of Data Science by examining its hybrid theoretical lineage, from the Universal Approximation Theorem to the No-Free-Lunch Theorems, with special emphasis on the fundamental Bayesian optimality results for both regression and classification. We argue that Data Science is in a vigorous \textit{gestational period}, characterized not by an absence of principles but by a creative tension between empirical pragmatism and deep mathematical theory. The Cross-Validation score emerges as the …

Learning Ordinal Geometry: Semantic–Aware Kernels For Ordered Categorical Data, Ernest Fokoue

Articles

Ordinal data arise ubiquitously in survey research, psychology, medicine, economics, and recommender systems, yet kernel methods for such data typically rely on either nominal encodings or arbitrary numeric codings. The former discards order information; the lat- ter imposes a fictitious metric structure. This paper develops a principled framework for kernel design on ordinal scales and introduces a new class of Semantic–Aware Ordinal Ker- nels (SAOK) that simultaneously capture ordinal order and semantic proximity between categories. We begin by formalizing order–preserving embeddings of finite chains and characterizing a broad family of chain distances that are conditionally negative definite. Through Schoen- berg …

On Fibonacci Ensembles: An Alternative Approach To Ensemble Learning Inspired By The Timeless Architecture Of The Golden Ratio, Ernest Fokoue

Articles

Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to the unfolding of leaves, this humble sequence reflects a universal grammar of balance. In this work, we introduce \emph{Fibonacci Ensembles}, a mathematically principled yet philosophically inspired framework for ensemble learning that complements and extends classical aggregation schemes such as bagging, boosting, and random forests \citep{Breiman1996Bagging, Breiman2001RandomForests, Friedman2001GBM, Zhou2012Ensemble, HastieTibshiraniFriedman2009ESL}. Two intertwined formulations unfold: (1) the use of normalized Fibonacci weights -- tempered through orthogonalization and Rao--Blackwell optimization -- …

Selecting Without Replacement From A Population Of Bands Of Serially Connected Objects, James E. Marengo, Dominick Banasik, Joseph Voelkel, David L. Farnsworth

Articles

The sampling procedure from a finite population of objects that are serially attached into bands is described and analyzed. One object is randomly selected and removed at a time, which results in that object’s band being broken into two bands or shortened by one object. The main result gives the probability of choosing an object that is part of a band of serially connected objects of any specified size at each stage of the selection process.

Ai-Powered Lawyering: Ai Reasoning Models, Retrieval Augmented Generation, And The Future Of Legal Practice, Daniel Schwarcz, Sam Manning, J. J. Prescott, Patrick Barry, David R. Cleveland, Beverly Rich

Articles

Generative AI is set to transform the legal profession, though its most promising uses and ultimate effects are still unclear. While AI models like GPT-4 improve efficiency, they can also “hallucinate” and may undermine legal judgment, particularly in complex tasks typically handled by skilled lawyers. This article examines two emerging AI innovations that may mitigate these concerns: Retrieval Augmented Generation (RAG), which grounds AI-powered analysis in legal sources, and AI reasoning models, which structure complex reasoning before generating output. We conduct the first randomized controlled trial assessing these technologies, assigning upper-level law students to complete legal tasks using a RAG-powered …

State Climate Superfunds, Rachel Rothschild

Articles

The harmful effects of climate change have already arrived in cities and states across America, with disasters increasing markedly in recent years along with more gradual environmental changes like sea-level rise and drought. To protect populations and natural resources, significant funding will be necessary for preventative measures as well as disaster response.

At present, it is states and ordinary taxpayers who must shoulder the enormous costs and planning for climate adaptation. A number of state legislators, however, have recently proposed enacting new laws that would require the companies who have most profited from fossil fuel usage to assist in funding …

Monitoring, Oversight, And Learning In Medical Ai, W. Nicholson Price Ii

Articles

When medical AI errs, it often goes unnoticed. If there’s a specific patient injury, and the link to AI is obvious, that problem might be reported to the Food and Drug Administration (FDA), but not always. And many other types of problems, like worse performance on specific groups or ineffective integration into health system workflows, simply don’t fall within the contours of regularized reporting. Even if they are noticed by the health system—far from a given—there’s no obvious way to share that information more broadly. Against this backdrop, there are justified calls for better oversight and reporting. But there’s the …

The Bandages Problem, James E. Marengo, Joseph G. Voelkel, David L. Farnsworth

Articles

A new probability problem, named the Bandages Problem, is described and solved. The problem involves repeatedly selecting and removing an item at random from a finite population that initially consists of a known configuration of single and paired items. For each selection, the probability that the chosen item is single is found. Generalizations are suggested.

Shrinkage Study In Photopolymerisable Hybrid Sol-Gel Through Holographic Patterning, Jamshed Aftab, Izabela Naydenova, Tatsiana Mikulchyk

Articles

Photopolymerisation induced shrinkage of holographic materials is one of the main factors which needs to be considered for designing holographic optical elements (HOEs) with high accuracy in light redirection with maximum efficiency. This work studies the shrinkage in photopolymerisable hybrid sol-gel (PHSG) by examining the properties of volume transmission gratings recorded in PHSG layers. It explores both the dependence of shrinkage on the holographic grating parameters (thickness, spatial frequency, slant angle) and the effect of material aging. By using the fringe-plane rotation model, shrinkage is found to have the maximum value of 1.37 % at 765 lines/mm (19.36° slant angle) …

Fixed Points In Linear Regression, David L. Farnsworth

Articles

There is a set of points in the plane whose elements correspond to the observations that are used to generate a simple least-squares regression line. Each value of the independent variable in the observations matches up with one of these points, which are called pivot or fixed points. The coordinates of the fixed points are derived, and the properties of the points are explored. All points in the plane that yield each of the fixed points are found. The role that fixed points play in regression diagnostics is investigated. A new mechanical device that uses linkages to model the role …

Pm2.5 Forecasting At U.S. Embassies And Consulates Worldwide Using Nasa Model Powered By Machine Learning, Junhyeon Seo, Alqamah Sayeed, Seohui Park, John Kerekes, Stephanie Christel, Mary Tran, Pawan Gupta

Articles

Air quality forecasting is crucial for public health, especially in rural, suburban, and developing areas lacking reliable monitoring data. Hybrid monitoring (surface, satellite, and models) offers a scalable, cost‐ effective solution for tracking pollution and trends. This work presents a machine learning model that integrates ground measurements with global model outputs assimilating satellite observations to forecast air quality. Ground measurements of fine particulate matter (PM2.5) from over 60 U.S. embassies and consulates were used to calibrate global model outputs for local air quality forecasting. Multi‐channel input data was prepared using the Goddard Earth Observing System forward processing for meteorology and …

Deleting Values May Either Increase Or Decrease Variance, David L. Farnsworth

Articles

The impact upon variance when a value is deleted is addressed. It is shown that the cutoff for the deleted value yielding an increase or a decrease in variance is approximately one standard deviation from the mean for a univariate random variable with equally distributed probability on a finite set of elements and for a univariate set of observations. The influence of truncation of the domain for such a discrete random variable and for observations is considered.

Integrating Standards For Infrastructure Improvement And Resilience In University Curricula, Lisa Greenwood, Jennifer Schneider, Sumita Mishra, Yewande S. Abraham, Shriram Karpoora Sundara Pandian

Articles

In today’s ever-changing world, we are increasingly vulnerable to shocks and stresses that disrupt industry and society. Persistent threats from natural and manmade hazards require our communities and infrastructure to be resilient despite possible disruption. Creating robust infrastructures is founded on operational and physical standards to withstand and respond to threats such as environmental exposures, climate change, and informational security breaches. The significant U.S. investment in infrastructure projects through the Infrastructure Investment and Jobs Act has amplified the need for professionals in engineering and related fields who – in addition to technical knowledge - possess the necessary knowledge and skill …

Quantifying The Role Of Active Listening And Reassurance In Virtual Health Coach Interactions, Ghulam Hussain, Brian Keegan, Robert Ross

Articles

Conversational Agents have the potential to support healthcare through coaching exercise routines, but are still lacking in demonstrating authentic social behaviours to support engagement. To this end, we present a series of experiments that we conducted in order to investigate how automated health care coaches can be more effective when their interaction style is tailored to demonstrate qualities associated with a good bedside manner, namely active listening and reassurance. To test this, we first developed a dataset of 135 dialogue excerpts from three distinct sources, i.e., original, handcrafted and LLMs, the latter two of which were tuned to demonstrate specific …

Evaluating The Ghg Emissions, Land Use, And Water Use Associated With Contemporary Dietary Patterns In The Republic Of Ireland, Daniel Burke, Paul Hynds, Anushree Priyadarshini

Articles

Dietary patterns are intrinsically linked to greenhouse (GHG) emissions, land use, and water use via food production systems. Analysing and comparing contemporary dietary patterns and their environmental impact is critical to identifying which should be promoted to enhance global sustainability. A cross-sectional survey of adult consumption patterns was conducted across Ireland with a representative sample size of 957 respondents. Subsequently, a farm-to-fork life cycle assessment (LCA) was employed via OpenLCA 2.0.4 to assess three primary environmental impacts (global warming, land use, and water use) across the population. Thirteen distinct dietary patterns were analysed: total population, rural, urban, self-reported (omnivore, flexitarian, …

Boden Lecture: Taxation Of Autonomous Artificial Intelligence, Reuven S. Avi-Yonah, Lucas Brasil Salama, Herbert Snitz, W. Robert Thomas

Articles

This Article proposes that tax can be a useful supplement to other measures to regulate Autonomous Artificial Intelligence (AAI) and limit its potential harmful effects. This proposal differs from command-and-control regulation of AAI along the lines of European Union legislation that may unduly limit the development of AAI. It also differs from existing proposals to tax AAI to generate revenue to help workers displaced by AAI programs, or to tax the data used by AAI The proposal is based on granting AAI programs like ChatGPT separate legal personhood, like corporate personhood, while incentivizing or requiring their corporate owner to place …

Ai And Tribal Court Practice, Matthew L.M. Fletcher

Articles

American Indian tribal court practice resides at the intersection of two difficult legal problems. First, because tribal justice systems are usually very young and dynamic, awareness and analysis of tribal law is underdeveloped. Second, because tribal nations are not governed by state or federal law, tribal law is culturally unique. Tribal court practitioners often find that even routine legal matters will involve questions of first impression in the jurisdiction. All of this is to say tribal court jurisprudence is intensely jurisgenerative.

Because tribal law is often unsettled or indeterminate, the costs of discovering and applying this law are occasionally high. …

The Future Of Ai Regulation In Drug Development: A Comparative Analysis, Gabriela Lenarczyk, Timo Minssen, W. Nicholson Price Ii, Arti Rai

Articles

As artificial intelligence (AI) transforms drug development, regulatory frameworks are evolving to oversee its implementation, particularly at the US Food and Drug Administration (FDA) and the European Medicines Agency (EMA). This paper makes three contributions to understanding emerging regulatory approaches. First, we offer a comparative analysis of how these agencies have responded to AI-driven advances, incorporating new US executive orders and the European Union (EU)’s AI Act. Second, we propose a novel analytical framework to understand regulatory divergence: the FDA’s flexible, dialog-driven model contrasts with the EMA’s structured, risk-tiered approach, reflecting broader institutional and political-economic differences. While the former encourages …

Environment Scan Of Generative Ai Infrastructure For Clinical And Translational Science, Hua Xu, Jiang Bian, Chunhua Weng, Yifan Peng, Betina Idnay, Zihan Xu, William G. Adams, Mohammad Adibuzzaman, Nicholas R. Anderson, Neil Bahroos, Douglas S. Bell, Cody Bumgardner, Thomas Campion, Mario Castro, James J. Cimino, I. Glenn Cohen, David Dorr, Peter L. Elkin, Jungwei W. Fan, Todd Ferris, David J. Foran, David Hanauer, Mike Hogarth, Kun Huang, Jayashree Kalpathy-Cramer, Manoj Kandpal, Niranjan S. Karnik, Avnish Katoch, Albert M. Lai, Christophe G. Lambert, Lang Li, Christopher Lindsell, Jinze Liu, Zhiyong Lu, Yuan Luo, Peter Mcgarvey, Eneida A. Mendonca, Parsa Mirhaji, Shawn Murphy, John D. Osborne, Ioannis C. Paschalidis, Paul A. Harris, Fred Prior, Nicholas J. Shaheen, Nawar Shara, Ida Sim, Umberto Tachinardi, Lemuel R. Waitman, Rosalind J. Wright, Adrian H. Zai, Kai Zheng, Sandra Soo-Jin Lee, Bradley A. Malin, Karthik Natarajan, Nicholson Price, Rui Zhang, Yiye Zhang

Articles

This study reports a comprehensive environmental scan of the generative AI (GenAI) infrastructure in the national network for clinical and translational science across 36 institutions supported by the CTSA Program led by the National Center for Advancing Translational Sciences (NCATS) of the National Institutes of Health (NIH) at the United States. Key findings indicate a diverse range of institutional strategies, with most organizations in the experimental phase of GenAI deployment. The results underscore the need for a more coordinated approach to GenAI governance, emphasizing collaboration among senior leaders, clinicians, information technology staff, and researchers. Our analysis reveals that 53% of …

Physicists As Environmental Experts, Rachel Rothschild

Articles

The question of which scientists are qualified to provide expert guidance in legal controversies is a perennial debate among scholars, judges, and lawyers. Scientists who participate in legal disputes can achieve enormous power and influence, not only over the case at hand but over long-term developments in legal doctrine. While these issues arise in many areas of the law, environmental litigation has been a particularly active site of contestations over epistemic authority. Courts have frequently relied on scientists to understand whether the government is justified in regulating pollution and who may be liable for environmental and public health harms.

This …

Clinicians In The Loop Of Medical Ai, W. Nicholson Price Ii

Articles

As medical AI begins to mature as a health-care tool, the task of governance grows increasingly important. Ensuring that medical AI works, works where it’s used, and works for the patient in the moment is a challenging, multifaceted task. Some of this governance can be centralized—in review by FDA or by national accreditation labs, for instance. Some must be local, performed by the hospital or health system about to use the product in their own, unique environment. But a large amount of governance is left to the individual provider in the room, the human in the loop who presumably knows …

Do Specialized Medical Llms Demand A Radically New Approach Under The Eu's Medical Device Regulation, Hannah Louise Smith, W. Nicholson Price Ii

Articles

We examine the arguments made by Onitiu and colleagues concerning the need to adopt a “backward-walking logic” to manage the risks arising from the use of Large Language Models (LLMs) adapted for a medical purpose. We examine what lessons can be learned from existing multi-use technologies and applied to specialized LLMs, notwithstanding their novelty, and explore the appropriate respective roles of device providers and regulators within the ecosystem of technological oversight.

Modelling The Formation Of Unslanted Holographic Gratings In Hybrid Photopolymer Media, Jack Lyons, Dana Mackey, Izabela Naydenova

Articles

The theoretical modelling of holographic recording in photopolymers has been an important tool in their optimisation. More complex, hybrid organic/inorganic photopolymers have been developed in pursuit of materials with higher sensitivity, low shrinkage, high dynamic range and environmental stability. Recent attempts to augment the existing models for the redistribution of inorganic nanoparticles in holographic recording were successful but there is still a knowledge gap in regards to modelling optical losses, mutual cross-diffusion, the formation of slanted holographic gratings and polymerization induced shrinkage in hybrid photopolymer media. This paper will describe a novel approach to modelling the formation of unslanted holographic …

High Tech Touts, Sherman J. Clark

Articles

This essay has three interrelated aims. First, it articulates a set of capacities I call virtues of attention—capacities for intuitive discernment, good judgment about what is worth sustained focus, and the ability to engage deeply with worthwhile things. These are eudaimonist virtues in that they help us live well, not merely act rightly. Second, the essay explores what I call poisonous persuasion: the idea that rhetorical appeals, especially those used in marketing, may not only succeed by appealing to certain desires or habits of mind but may also deepen and entrench them. Third, I bring these insights together to examine …

Synthetic Data Generation Of Health And Demographic Surveillance Systems Data: A Case Study In A Low- And Middle-Income Country, Dorcas G. Mwigereri, Nigel T. Kamotho, Akbar K. Waljee, Ryan T. Rego, Eileen M. Weinheimer-Haus, Farhana Alarakhiya, Anthony K. Ngugi, W. Nicholson Price, Ji Zhu, Stephen Peter Wong, Geoffrey H. Siwo

Articles

Objective: To evaluate effectiveness of open-source generative models in producing high-quality tabular synthetic data using a Health and Demographic Surveillance System (HDSS) dataset from rural Kenya, as a proof of concept in a low- and middle-income (LMIC) setting.

Materials and Methods: Three open-source models (CTGAN, TableGAN, and CopulaGAN) were used to generate synthetic data from the Kaloleni/ Rabai HDSS dataset. To assess the quality of the synthetic datasets generated by each model, we performed fidelity, utility, and privacy tests.

Results: CTGAN outperformed the other models, producing synthetic data that closely mirrored the statistical properties of the real dataset while preserving …