Digital Commons Network^™

Artificial Intelligence, Society 5.0 And Smart City Adaptation Initiatives For Businesses: An Integrated Approach, Inês A.M. Gil, Fernando A.F. Ferreira, Neuza C.M.Q.F. Ferreira, Florentin Smarandache, Momtaj Khanam, Tugrul Daim

Branch Mathematics and Statistics Faculty and Staff Publications

The unprecedented migration of populations to urban areas has created major challenges for municipalities and service providers. To address these issues, decision-makers must embrace smart city and Society 5.0 paradigms, both of which focus on adaptability and sustainable development. Artificial intelligence (AI) plays a pivotal role by expanding service capacity, enabling automation, and processing vast data to align urban development with the UN’s Sustainable Development Goals (SDGs). This paper develops a multi-criteria analysis system designed to support decision-making in complex socio-technological contexts. Using cognitive mapping and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique within a neutrosophic environment, the study …

Autopoietic Energy Transition Towards Clean And Renewable Energy For Developing Countries, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The global economy's reliance on energy supply and distribution necessitates a shift towards clean and renewable energy sources. This article explores how the economies of energy producers and consumers can be better modeled through the lens of autopoiesis, a concept developed by Humberto Maturana and further elaborated by Fritjof Capra (cf. Web of Life). By viewing energy systems as self-producing and self-maintaining entities, we can gain insights into the dynamics of energy transition in developing countries and identify strategies for fostering sustainable and resilient energy ecosystems.

Modelado Causal De La Violencia En El Área Metropolitana De Guayaquil: Evidencia Neutrosófica Y Análisis De Condiciones Necesarias, Maikel Y. Leyva Vázquez, Lorenzo Cevallos-Torres, Alfonso Guijarro Rodríguez, Douglas Iturburu-Salvador, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La violencia urbana en el área metropolitana de Guayaquil plantea desafíos persistentes para el bienestar social y la gobernanza. Este estudio integra tres fuentes de evidencia para clarificar qué factores son necesarios y qué niveles mínimos habilitan altos niveles de violencia. Primero, se aplica stance detection con representación neutrosófica para construir un prior (T, I, F) de la literatura. Luego, evaluamos condiciones necesarias mediante fsQCA (inclusión difusa 𝑌⊆𝑋, umbral de consistencia ≥ 0.90) y estimamos umbrales (bottlenecks) con NCA (CE-FDH, CR-FDH, permutaciones). Usamos la misma matriz fuzzy en ambos métodos para asegurar coherencia. Con una encuesta a 179 jóvenes de …

Ppg-Based Sleep Stage Classification Using Pulse Wave Feature Fusion And Explainable Ai, Florentin Smarandache, Satyasri Akula, Saleh Alzahrani, Farrukh Arslan, Amir Ijaz

Branch Mathematics and Statistics Faculty and Staff Publications

Sleep monitoring plays a crucial role in understanding and managing various health conditions, including sleep disorders, cardiovascular diseases, and mental health. Traditional sleep monitoring methods rely on Electroencephalography (EEG) and Polysomnography (PSG) in clinical settings. However, these methods are expensive, difficult to administer, and unsuitable for home-based monitoring. In recent years, photoplethysmogram (PPG) has emerged as a promising noninvasive technology that is widely used in wearable devices and holds great potential for sleep assessment. Yet, most current sleep monitoring methods rely on deep learning models, which are inherently "black-box" and challenging in the clinical decision-making process. In this paper, we …

A Critical Evaluation Of The Criticisms Against Neutrosophic Statistical Methods, Muhammad Aslam, Abdulrahman Alaita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic statistical analysis has gained attention for incorporating the degree of indeterminacy when analyzing imprecise and interval data under uncertainty—an aspect often overlooked by classical statistics, fuzzy statistical analysis, and interval statistics. Recently, critical discussions have emerged regarding the use and applications of neutrosophic statistics, with some questioning its usefulness and validity. In this paper, we present a critical assessment of the existing literature, focusing on areas where misunderstandings and misinterpretations of neutrosophic statistical methods have occurred. We also examine flawed comparisons made between the results of neutrosophic statistics and interval statistics. Furthermore, substantial issues have been identified in the …

A Neutrosophic Approach To Social Phenomena, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sociology has long sought to understand human societies and the social behaviors within them. It explores the organization, structure, dynamics, and transformations of society over time. However, traditional sociological methods face significant challenges in addressing the complexity and indeterminacy inherent in social data—data that is often ambiguous, incomplete, and contradictory. The Neutrosociology offers a novel approach to studying and modeling social phenomena by employing mathematical and philosophical tools that can accommodate uncertainty.

A Family Of Neutrosophic Estimators For Estimating Mean: An Application To Real Data, Bavita Singh, Abhishek Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the realm of sample survey research, the classical statistics approach primarily deals with precise and definitive types of data to estimate population parameters when additional information is available. However, this approach fails when faced with data indeterminacies. To address such ambiguities, neutrosophic statistics emerges as an extension of both fuzzy and classical statistics. Thus, in light of the challenges posed by indeterminacy in sampling, we have introduced a proficient neutrosophic class of estimators, with and without Searls technique (optimization tool) for estimating the mean utilizing additional (ancillary) information under neutrosophic simple random sampling (NeSRS). The expression for the Bias …

Prólogo Al Número Especial “Neutrosophic Computing And Machine Learning”, Vol. 40, 2025, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel Basset

Branch Mathematics and Statistics Faculty and Staff Publications

Esto es un prólogo al número especial de "Neutrosophic Computing and Machine Learning" presenta una selección de trabajos significativos sobre enfoques neutrosóficos y plitogénicos en ciencia de datos y análisis multivariante de la IX Conferencia Iberoamericana de Biometría. La conferencia, celebrada en Quito, Ecuador, del 8 al 9 de julio de 2025, reunió a más de 250 expertos de 13 países. El éxito del evento fue resultado de la colaboración entre la Universidad Estatal de Milagro (UNEMI) de Ecuador y la Universidad de Salamanca (USAL) de España. Los artículos de este volumen exploran la relación entre la estadística clásica y …

Neutrosophic Stance Detection And Fsqca-Based Necessary Condition Analysis For Causal Hypothesis Assessment In Ai-Enhanced Learning, Jesús Rafael Hechavarría-Hernández, Maikel Y. Leyva Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study addresses the ambiguities in empirical findings on artificial intelligence (AI) in education by proposing a new methodological framework that combines neutrosophic stance detection and Fuzzy Set Qualitative Comparative Analysis (fsQCA). This approach explicitly models truth, indeterminacy, and falsity, allowing for the synthesis of contradictory research. The authors evaluated four causal hypotheses related to AI-based learning, using a survey of 24 university participants to explore the necessary conditions for perceived learning improvements. The results indicate that the digital divide is a perfectly necessary condition for effective AI-enhanced learning. The findings also reveal that AI feedback and AI platform use …

A Neutrosophic Exploration Of Creative Ideational Dynamics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Philosophy has always tried to illuminate the complexity of existence, but often faced its own paradoxes. The emergence of philosophical schools and concepts, along with their arguments, reflect the dynamic interaction of ideas. This short note explores some nuanced principles governing philosophical thought, summarized in the proposed “philosophical formulas.” These formulas are intended to mathematically and conceptually express the tensions, complementarities, and movements intrinsec in a given philosophical system.

A Position Indicator With Applications In The Field Of Designing Forms With Artificial Intelligence, Ovidiu Ilie Șandru, Florentin Smarandache, Alexandra Șandru

Branch Mathematics and Statistics Faculty and Staff Publications

The indicators used so far within the Theory of Extension can be synthetically expressed by the notion of “position indicators”. More exactly, these indicators can be grouped in two main sub-categories: point-set position indicators and point-two sets position indicators. The secondary goal of this paper is to define these classifications, while the primary goal is that to extend the two notions to the most general notion of set-set position indicator.

Approches Neutrosophiques Et Plithogéniques En Science Des Données Et Analyse Multivariée : Contributions De La Ixe Réunion Ibéro-Américaine De Biométrie, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel-Basset

Branch Mathematics and Statistics Faculty and Staff Publications

Ce numéro spécial de "Neutrosophic Sets and Systems" rassemble une sélection de travaux remarquables présentés lors de la IXe Réunion Ibéro-américaine de Biométrie, qui a eu lieu les 8 et 9 juillet 2025 à Quito, en Équateur. Sous la direction d'une équipe éditoriale de prestige, ce volume explore l'application des approches neutrosophiques et plithogéniques dans divers domaines tels que la biométrie, la bioinformatique, la santé publique, l'éducation et l'économie. Les articles mettent en lumière la convergence entre les statistiques classiques et l'intelligence artificielle, illustrant comment les méthodes neutrosophiques offrent des outils puissants pour modéliser l'incertitude et la complexité des données …

Competition Super-Hypergraphs: Revealing Hierarchical Competition In Real-World Networks, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory provides a powerful language for modeling pairwise connections through vertices and edges [9, 20]. Hypergraphs generalize this idea by permitting hyperedges that join any number of vertices simultaneously [7], while super-hypergraphs iterate the Power-set operation to capture multi-level, hierarchical relationships among hyperedges [40, 22]. A competition hypergraph associates each prey species with a hyperedge containing all its predators, thereby encoding multi-way competition in ecological networks. In this work, we introduce the competition super-hypergraph, which lifts the competition concept to higher tiers of aggregation. We present its formal definition, explore theoretical properties, and illustrate its practical use in real-world …

Cvitlnn: A Hybrid Approach Based On Vision Transformer And Liquid Neural Network For Covid-19 Detection, Muhammad Waqaq, Florentin Smarandache, Muhammad Yasir, Farrukh Arslan, Anum Ali

Branch Mathematics and Statistics Faculty and Staff Publications

The COVID-19 pandemic has underscored the need for accurate and rapid diagnostic tools to assist clinical decision-making. Conventional deep learning models for COVID-19 detection in Chest X-Ray (CXR) images face challenges in poor generalization across imaging conditions and high computational demands. To address these issues, this study proposes CviTLNN, a novel hybrid model combining Vision Transformers (ViTs) and Liquid Neural Networks (LNNs) to improve feature extraction and classification. Specifically, CviTLNN employs a ViT with 24 transformer encoder blocks for efficient extraction of spatial features. The self-attention mechanism of ViTs effectively captures global and local dependencies in CXR images. Furthermore, …

Multipliers On Weighted Sequence Spaces, Gilbert Acheampong, Raymond Cheng

Mathematics & Statistics Faculty Publications

The space ℓp,α of complex sequences a = (a0, a1,a2,...) for which

[[formula omitted]]

is studied. Each such sequence can be identified with the analytic function with power series

[[formula omitted]]

In this setting, the point evaluation and the difference quotient mappings are shown to be bounded; the cases are identified in which ℓp,α is boundedly contained in ℓr,β. Conditions on the parameters are derived for the analytic functions of ℓp,α to have radial limits almost everywhere on the boundary, and for ℓp,α to be an algebra. Smoothness properties of the boundary function are investigated. Basic properties of multipliers on …

Golden Spirals Everywhere?, John Adam

Mathematics & Statistics Faculty Publications

The article explores different types of spirals, including Archimedean, hyperbolic, and logarithmic spirals, with a focus on the golden ratio and golden spirals. It discusses the misconception that golden rectangles and spirals can be found in various natural and man-made objects, emphasizing the importance of understanding the properties of logarithmic spirals. The text provides mathematical equations for logarithmic spirals and poses questions for readers to explore the concept further. The author, John Adam, invites readers to engage in Fermi Questions and submit ideas for consideration.

Model-Free Organization Of Patient Reported Outcomes Data: Geometrical Rep-Resentation Of The Modified Compartmen-Talization Method, Manasi Sheth, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

There is a recent advancement in the field of mathematics and statistics to understand the geometry or connectedness of the data due to the massive amounts of data being generated. The data provided for analyses are usually very large and need to be organized and minimized in order to make it more useful and meaningful. In biostatistics or medical field, it is important for patients to have access to high-quality, safe and effective and/ or efficacious medical products. It is quite necessary to ascertain that the patients and their care-partners stay at the center of the regulatory decision-making process. In …

A Decision-Space Model Explains Context-Specific Decision Making, Dirk W. Beck, Cory N. Heaton, Luis D. Davila, Lara I. Rakocevic, Sabrina M. Drammis, Danil Tyulmankov, Atanu Giri, Shreeya Umashankar Beck, Qingyang Zhang, Michael Pokojovy, Kenichiro Negishi, Alexis A. Salcido, Neftali F. Reyes, Andrea Y. Macias, Serina A. Batson, Paulina Vara, Raquel J. Ibáñez Alcalá, Safa B. Hossain, Graham L. Waller, Laura E. O'Dell, Travis M. Moschak, Ki A. Goosens, Alexander Friedman

Mathematics & Statistics Faculty Publications

Optimal decision-making requires consideration of internal and external contexts. Biased decision-making is a transdiagnostic symptom of neuropsychiatric disorders. We created a computational model demonstrating how the striosome compartment of the striatum constructs a context-dependent mathematical space for decision-making computations, and how the matrix compartment uses this space to define action value. The model explains multiple experimental results and unifies other theories like reward prediction error, roles of the direct versus indirect pathways, and roles of the striosome versus matrix, under one framework. We also found, through new analyses, that striosome and matrix neurons increase their synchrony during difficult tasks, caused …

A Bridge Too Low: Solutions For Fermi Questions, May 2025, John Adam

Mathematics & Statistics Faculty Publications

The article discusses a low bridge in Keswick, England, near the River Greta, with an arch shaped like a semiellipse. It presents Fermi questions related to the bridge's dimensions, such as the maximum distance a person of a certain height can walk under it without hitting their head. The solutions involve mathematical calculations and approximations, including the use of formulas provided by the Indian mathematician Srinivasa Ramanujan.

Untangling The Classification Of Surfaces: An Accessibility-Centered Perspective On Topology, Charlotte N. Richards

Pitzer Senior Theses

Mathematics has clear benefits in education, from preparing students for future careers to teaching them how to problem-solve. While mathematics achievement has been falling in recent decades, students claim that the problem is not the mathematics itself, but the ‘boring’ classroom material that feels removed from real life. More advanced mathematics topics, such as topology, could offer a solution, as their applications lie in countless fields. However, topology has been restricted to upper-level mathematics, disregarding the potential benefits of making this material broadly reachable for a junior high-school audience. In this paper, we analyze five different proofs of the theorem …

Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.

Permutations Minimizing The Number Of Collinear Triples, Joshua Cooper, Jack Hyatt

Faculty Publications

We characterize the permutations of Fq whose graph minimizes the number of collinear triples and describe the lexicographically-least one, confirming a conjecture of Cooper-Solymosi. This question is connected to Dudeney’s No-3-in-a-Line problem, the Heilbronn triangle problem, and the structure of finite plane Kakeya sets. We discuss a connection with complete sets of mutually orthogonal latin squares and state a few open problems primarily about general finite affine planes.

The Algebra Behind Magic, Lois Carpenter

Undergraduate Research Awards

Card Tricks have long been a staple in the common magician’s repertoire, and while many tricks can be explained through sleight of hand alone, others rely on seemingly random shuffling methods that leave the magician with significant control over the deck. Applied card magic (frequently referred to as ‘cheating’) makes significant use of this ability. Thus, the utility of this topic is clear- anyone with basic mastery of perfect shuffles has complete control over the arrangement of cards in a deck, and with it a fundamental advantage against other players in any game of cards. While most perfect shuffles are …

Completing Multi-Latin Rectangles Via Factors With Prescribed Degrees In Bipartite Graphs, Amin Bahmanian

Faculty Publications – Mathematics

Let Q be an n x n array whose top left r x s sub‐array L is filled with a set of k different symbols such that each cell of L contains λ symbols. In this note, we find conditions under which each empty cell of Q can be filled with λ symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol
occurs at most λ times in each row and column of Q. To prove this result, we establish a new criterion for a bipartite graph to have …

Developments On Quantum Phase Space Dynamics And Foundations, Gabriel Nowaskie

Mahurin Honors College Capstone Experience/Thesis Projects

This work explores the development and unification of quantum theory within phase space, with a particular focus on new mathematical structures and solution techniques that extend the standard quantum formalism. Building upon the Quantum Phase Space Representation (QPSR) introduced by Torres-Vega and Frederick, we present several advancements that address longstanding gaps in the formulation and solvability of quantum systems in this framework. We introduce the Half-Transform Ansatz, a novel method for solving the Time-Independent Schrodinger Equation by recasting it into a hypergeometric form, enabling the application of the Nikiforov-Uvarov method. This approach is demonstrated through the analysis of quarkonium systems …

Algebra Structures For The Koszul Homology Of Minimal Intersections, Kathryn A. Grebel

Mathematics Dissertations - Archive

The Koszul homology of a local ring is a powerful tool in commutative algebra as it provides information on the structure and properties of the ring. In this research, we explore the relationship between quotients of regular local rings and their Koszul homology algebra. One such relationship is detailed by the Tate-Assmus theorem, which asserts, in part, that a ring is a complete intersection if and only if the Koszul homology is generated by its degree 1 homology elements. An objective of this research is to examine and identify the properties of a minimal intersection and its Koszul homology algebra. …

Two Network Flow Problems: Volume Inequalities For Flow Polytopes Of Full Directed Acyclic Graphs; Optimal Additions To The Low-Stress Bike Network In Lexington, Kentucky, James F. Mcelroy

Theses and Dissertations--Mathematics

This dissertation addresses two distinct problems related by their foundation in network flows. The first problem concerns volumes of flow polytopes of directed acyclic graphs with out-degree sequence (3,2,...,2,0). It is proved that there is an interchange operation on the edge set of these graphs that induces a partial order on the graphs isomorphic to a Boolean algebra, and that moving up through this partial order decreases (weakly) the volumes of the corresponding flow polytopes. This result is reinterpreted in the context of linear extensions for posets that are bipartite non-crossing trees.

The second problem develops a discrete optimization model …

Novel Generative And Language Model Architectures With Applications, Edison Mucllari

Theses and Dissertations--Mathematics

This dissertation investigates novel architectures to address fundamental challenges in machine learning, particularly focusing on transformer models, recurrent neural networks, GAN and continual learning and their applications in natural language processing and computer vision. We propose the Neumann-Cayley Gated Recurrent Unit (NC-GRU), which leverages a Neumann series-based Scaled Cayley transformation to maintain orthogonal weight matrices, effectively mitigating exploding gradients problems while improving long-term memory retention across prediction tasks. We demonstrate the practical applications of NC-GRU by implementing our proposed architecture into an autoencoder to derive neural molecular fingerprints. Building upon these advancements, we turn our attention to the transformer architecture, …

Blow-Ups And Projectivized Toric Vector Bundles, Sara Church

Theses and Dissertations--Mathematics

This dissertation is set in the intersection of toric geometry, tropical geometry, and the theory of vector bundles. We focus on the geometry of projectivized toric vector bundles and their connections to Mori dream spaces, matroid theory, and tropical geometry. We generalize previous results on the quotient construction of Gonzalez, Hering, Payne, and Suss (GHPS) by introducing a new approach to describing the geometry of these bundles via associated blow-ups. Additionally, we examine tautological bundles arising from representable matroids and establish connections between their geometry and the wonderful compactification. Finally, we consider the case where Klyachko filtrations have maximal steps …

The Computational Algebra Of Conformal Blocks, Casey B. Hill

Theses and Dissertations--Mathematics

Conformal blocks are objects in quantum field theory that arise from conformal trans- formations, which are symmetries that preserve angles but not length. This aspect of conformal field theory has various interactions with algebraic geometry.

In this dissertation, we explore the underlying algebra and geometry of spaces and algebras of conformal blocks over SLn. We then use this information along with techniques from combinatorial commutative algebra, algebraic geometry, and representation theory to find a presentation of the algebra of SL4-conformal blocks. With this presentation, we then use computational methods to learn about some of the geometric properties of this algebra.