Physical Sciences and Mathematics Commons^™

Quantum General Relativity V2, James Glimm, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

We construct a quantum general relativity theory.. The construction includes specification of a cosmological model. Based on type Ia supernova data, the model has zero dark energy and zero cosmological constant.

The analysis is at the level of theoretical physics, with some mathematical details omitted.

Brst Conserved Moments For Fluids, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

This note adds a missing proof for an assertion in the original paper Gauge Invariance and Repeated Time Isolated Solution Discontinuities.

The assertion is that under weak limits and within a constant energy isosurface, enstrophy is conserved up to losses due to viscous dissipation.

According to the BRST theory for quantum Yang-Mills fields, the conserved moments are exactly those with infinite vacuum expectation values. Application of the BRST theory to fluids is explored. The BRST restriction to the loop expansion (fixed space) is justified by the reqirement that a perturbative expansion can be constructed. In this case the theory predicts …

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure general relativity (quantum or classical) is one lacking in matter. Such a field has a Lorentzian space time geometry. A renormalization perturbative expansion, truncated to all finite orders, establishes both the quantum and the general relativity theory with full mathematical rigor.

Weak Solutions Of The Navier-Stokes Equation And Their Euler Limits, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The existence of a weak solution of the incompressible isothermal Navier-Stokes equation with given initial conditions in the Sobolev space $\mathcal{H}_{-2}$ for energy fluctuations and in $\mathcal{H}_{-3}$ for enstrophy fluctuations is assumed. The existence is uniform with respect to the Euler limit of zero viscosity $\nu$. Thus, existence of weak solutions of the Euler equation with given initial conditions is established, and these Euler solutions are the zero viscosity limit of Navier-Stokes solutions, provided the Navier-Stokes solutions exist.

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure quantum general relativity field is one lacking in matter. Such a field has a Lorentzian space-time geometry. A renormalized perturbation expansion, truncated to all finite orders, establishes  the existence of pure quantum general relativity with full mathematical rigor

The Pure Yang-Mills Field. I: Eistence, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

Two pure Yang-Mills quantum gauge field theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.

The construction is based on the axial gauge, ghost states, the BRST framework and Gribov extension of the Hamiltonian, with a loop expansion cutoff to all finite orders for the dynamics.

The construction is established by renormalized perturbation theory to all finite orders.

The construction depends on an assumed principle of a maximum rate of entropy production

The Pure Yang-Mills Field, \, Iia: The Axioms, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A previously constructed pure Yang-Mills quantum gauge field theory is shown to satisfy all Osterwalder Schrader axioms.

Non-Smooth Solutions Of The Navier-Stokes Equation And Their Means, James Glimm, Jarret Petrillo

Department of Applied Mathematics & Statistics Faculty Publications

Non-smooth (finite time blowup) Leray-Hopf solutions of the incompressible Navier-Stokes equation are constructed. The initial data for blowup is characterized by nonzero energy related turbulent fluctuations. The construction occurs in a finite periodic cube T3. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation.

Scaling Laws, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

Scaling laws, accurate to all orders and for intermediate times, are constructed for Navier-Stokes and Euler fluids and for quantum Yang-Mills fields. A maximum entropy principle is assumed. A finite periodic spatial volume is assumed.

Conventional renormalization group scaling is accurate to all orders in a large time asymptotic limit, but it fails at intermediate times at less than leading order due to blowups and a possible resetting of the gauge group.

The extension to quantum general relativity is indicated.

The Pure Yang-Mills Field: Repeated Blowups, James Glimm, James G. Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The temporal scaling of the quantum Yang-Mills solution is characterized by analytic solutions for a limited time interval, each ended by a discontinuity (blowup).

For general initial conditions, there will be a series of blowups and a possible resetting of the gauge group..

The principle of a maximum rate of entropy production is assumed. A finite periodic spatial volume is assumed.

The Boson Yang-Mills Field: The Loop Expansion, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

This paper demonstrates convergence of the loop expansion for Yang-Mills fields.

The loop construction of perturbation theory is based on the axial gauge, ghost states, the BRST framework and the Gribov extension of the Hamiltonian, with the loop expansion perturbatively renormalizable.

The construction is established by renormalized perturbation theory convergent to all finite orders.

Two distinct Yang-Mills theories are constructed, one based on short distance asymptotics and the other based on long distance asymptotics.

The construction depends on an assumed principle of a maximum rate of entropy production.

The paper has sufficient generality to include existence for all cases that …

The Pure Yang-Mills Field: Axioms And The Mass Gap, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The infinite volume limit is constructed based on previously constructed finite volume pure Yang-Mills quantum gauge field theories. For this limit theory, Osterwalder-Schrader axioms are verified and the existence of a mass gap in the energy spectrum is proven.

Requirements for the Millennium Yang-Mills prize are fulfilled.

Validity Assessment Of Resting Heart Rate Variability From The Garmin Health Snapshot, Kayla M. Porter, Andrew Flatt

Honors College Theses

Purpose: To assess the agreement between the Garmin Forerunner 265 (a commercially available sports watch) and a single-channel electrocardiographic (ECG) chest strap for determining resting heart rate variability (HRV). Secondary aims were to assess the impact of skin tone and body position on measurement accuracy.

Methods: Young adults (n = 30, 57% women) aged 18–39 years without known cardiovascular conditions and without tattooing or scarring on the dorsal left wrist were recruited. HRV was recorded simultaneously using ECG and the Forerunner 265’s optical sensor during Garmin’s 2-minute “Health Snapshot.” Measurements were obtained in three standardized positions: supine, seated, and standing. …

Rydberg Atom Arrays For Electric Field Sensing, James P. Hamilton

Honors College Theses

Rydberg atoms, hydrogen-like atoms that can be excited to states of high principal quantum number that carry correspondingly large electric dipole moments, have become leading candidates for precision electric field sensing. Arrays of such atoms, each trapped in a focused laser beam called an “optical tweezer,” are a particularly promising platform, since the strong dipole-dipole interactions between neighboring atoms provide a resource unavailable in a single-atom sensor. This thesis develops a theoretical and numerical framework for electric field measurement in small Rydberg atom arrays. We begin with a two-level model of a single atom, derive the Hamiltonian and equations of …

Development And Evaluation Of A Gc-Msms Method For The Quantification Of Gamma Hydroxybutyrate In Hair, Jacob Robert Keller

Theses: Doctorates and Masters

Gamma (γ)-hydroxybutyrate (GHB) is an endogenous short-chain fatty acid, and is of forensic importance due to its use in drug facilitated sexual assault (DFSA). Exogenous GHB has a limited window of detection in blood (1-hour) and urine (12-hours). Testing hair allows detection of drugs months after ingestion. This thesis contains a literature review which compares published methods which determine concentration of endogenous GHB in hair to determine which procedures are suitable for experimental comparison. The aims of this thesis were to develop a GC-MS-based method for the detection of GHB, test various methods to improve extraction, determine linearity, precision, accuracy, …

Rapid Classification And Quality Assessment Of Citrus Essential Oils Via Machine-Learning-Assisted Raman Spectroscopy, Yong Xuan Hong, Jia Wei Tang, Jie Chen, Yun Yun Xie, Zhang Wen Ma, Qing Hua Liu, Liang Wang

Research outputs 2022 to 2026

Citrus essential oils (EOs) require accurate identification and assessment to ensure authenticity and consistency. However, conventional techniques such as gas chromatography (GC) and mass spectrometry (MS) are time-consuming and expensive, highlighting the need for novel analytical methods. This study proposes an approach for EOs detection using Raman spectroscopy (RS) combined with machine learning (ML) algorithms. Six citrus EOs underwent an evaporation experiment, with Raman spectra collected at five time points and GC-MS was used to analyze compositional changes at the starting and ending points of evaporation as a standard reference. Five ML algorithms were developed to identify differences among EOs …

Sparse Gradient Training For Recommender Systems, Yunke Qu, Liang Qu, Tong Chen, Xiangyu Zhao, Jianxin Li, Hongzhi Yin

Research outputs 2022 to 2026

Recommender systems are widely applied in numerous online platforms such as shopping and social media platforms. They typically utilize large embedding tables that map users and items to dense vectors of uniform sizes. As the number of users and items continues to grow, this design leads to significant memory consumption and computational inefficiencies. This challenge is particularly pronounced in scenarios such as federated learning, where model parameters are updated locally on edge devices with limited computational resources before being transmitted to a central server for aggregation. Numerous approaches have been proposed to address this issue, among which embedding pruning methods …

Priority Questions For The Next Decade Of Blue Carbon Science, Peter I. Macreadie, George E. Biddulph, Pere Masque, Hilary Kennedy, Jimena Samper-Villarreal, J. Patrick Megonigal, Hannah K. Morrissette, Tania E. Romero-Gonzalez, Vanessa Hatje, Jana Friedrich, Sigit D. Sasmito, Kenta Watanabe, Inés Mazarrasa, Dorte Krause-Jensen, Janine B. Adams, Miguel Cifuentes-Jara, Ariane Arias-Ortiz, Andre S. Rovai, Milica Stankovic, Kirsten Isensee, Ana M. Queirós, Luzhen Chen, Jorge Herrera-Silveira, Catriona L. Hurd, Rashid Ismail, Ken W. Krauss, Anna Lafratta, Maria M. Palacios, William E.N. Austin

Research outputs 2022 to 2026

Blue carbon ecosystems, classically defined as mangroves, tidal marshes and seagrasses, but increasingly expanded to include ecosystems such as tidal flats, macroalgal forests and shelf sediments, contribute to climate change mitigation and biodiversity support. Here, seven years after the last global assessment of research priorities, we conducted a priority-setting exercise to identify persistent knowledge and implementation gaps, and the strategic priorities that must be addressed to enable scalable, high-integrity and equitable management of blue carbon ecosystems in a rapidly evolving policy and finance landscape. The highest priority focuses on managing blue carbon ecosystems to support coastal communities while integrating traditional …

The Value Of Saltbush Revegetation For Biodiversity In A Highly Fragmented Landscape, Robert A. Davis, Michael D. Craig, Tim S. Doherty, Jonathan D. Majer, Eddie J.B. Van Etten

Research outputs 2022 to 2026

Secondary salinization is a significant global issue affecting up to 1 billion hectares of land, impacting biodiversity and particularly vegetation. One form of revegetation that can provide a return to landholders is saltbush (Atriplex spp.), which provides forage for a wide range of livestock. The effectiveness of saltbush plantings in providing useful habitat for fauna in agricultural landscapes suffering from secondary salinity is poorly understood. We aimed to address this knowledge gap by surveying bird, ant, and spider communities, and quantifying vegetation structure and floristic composition in saltbush and native woodlands in agricultural landscapes affected by secondary salinization in Western …

A Knowledge-Driven, Ai-Assisted Cyber Defence Framework For Iomt Remote Patient Monitoring, Kulsoom S. Bughio, David M. Cook, Abdul M. Unar

Research outputs 2022 to 2026

The rapid adoption of Internet Medical Things (IoMT) technologies in remote patient monitoring has reshaped healthcare delivery by enabling continuous, real-time clinical observation outside traditional care settings. However, this shift has also expanded the cyber-attack surface across heterogeneous, resource-constrained medical devices, wireless networks, cloud services, and third-party platforms. In cyber warfare, healthcare has become an incorporated target of geopolitics, with hospitals, remote monitoring systems, and emergency health systems being used to broaden the attack surface for adversaries to exploit. Existing security approaches for IoMT environments remain largely manual, fragmented, and reactive, limiting their effectiveness in dynamically assessing vulnerabilities and supporting …

2025 - Tennessee Climate Snapshot, Tennessee Climate Office, East Tennessee State University

Tennessee Climate Office Monthly Reports

No abstract provided.

Semi-Supervised Learning For Annotation And Representation Of Single-Cell Rna Sequencing And Spatial Transcriptomics Data, Haoran Liu

Dissertations

Semi-supervised learning has emerged as a powerful paradigm for analyzing single-cell RNA sequencing (scRNA-seq) and spatial transcriptomics (ST) data, where full annotation is often costly or impractical. scRNA-seq technologies measure the expression of thousands of genes across tens of thousands of cells, whereas ST additionally captures the spatial coordinates of gene expression within intact tissue sections. Annotation is a key step in both scRNA-seq and ST analysis pipelines, aiming to identify cell types, spatial domains, and latent biological structures. However, most existing annotation approaches rely on separate clustering methods that are typically fully unsupervised and fail to leverage side information …

Beyond Words: A Systematic Multimodal Framework For Text, Images, And Extreme Helpfulness In Online Reviews, Alvaro J. Aguado Marin

Dissertations

Online product reviews have become increasingly multimodal, combining text with media-rich elements such as images. However, academic research has largely examined textual features in isolation, overlooking how visual content and its interaction with text shape perceived helpfulness. This dissertation addresses that gap by developing and empirically validating a comprehensive framework capturing how textual, visual, and contextual features collectively influence review evaluation. Grounded in the Elaboration Likelihood Model (ELM) and extended through the Text-Image Elaboration Likelihood Model (TI-ELM), the framework advances understanding of how consumers process content from both user- and business-generated sources. It also lays the foundation for examining emerging …

Computational Design Of Nanoporous Materials For The Adsorption Of Per- And Polyfluoroalkyl Substances, Daniel D. Mottern

Dissertations

Per- and polyfluoroalkyl substances (PFAS) are a large family of chemicals that have seen wide usage due to their fluorinated carbon backbone. The presence of strong C-F bonds in the backbone lends PFAS molecules high thermal and chemical stability, as well as strong hydrophobicity and lipophobicity. This combination of properties has led to heavy use of PFAS as surfactants, non-stick coatings, and aqueous foam forming films and flame retardants. However, these properties bring their own consequences. The high chemical and thermal stability of PFAS renders them persistent, with the C-F bonds resisting naturally occurring forms of degradation. Existing forms of …

Computational Methods For Single-Cell And Multi-Omic Data Integration And Regulatory Network Inference, Jianlan Ren

Dissertations

Single-cell and multi-omic technologies have transformed the dissection of cellular heterogeneity and regulatory dynamics in health and disease. However, the high dimensionality, technical variability, and biological complexity of these datasets present significant challenges for integration, annotation, and interpretation. In this dissertation, a suite of computational approaches is introduced to address key problems in single-cell and multi-omic data analysis through model-based innovations and applied statistical frameworks.

First, a constrained deep learning framework for single-cell data integration, label transfer, and clustering is proposed. By incorporating biologically motivated constraints into the training process, robust performance is achieved across simulated and benchmark datasets spanning …

Data-Driven Analysis And Atomistic Simulations Of Next-Generation Materials For Energy Conversion And Storage, Yuliang Shi

Dissertations

Metal-organic frameworks (MOFs), with their modular architectures and tunable properties, represent an especially rich domain for accelerated material design and discovery for a range of diverse applications. Within this class of multifunctional materials, two-dimensional (2D) electrically conductive MOFs (EC MOFs) are of particular interest, as their 7r-stacked layered structures combine permanent porosity with electronic conductivity, enabling potential breakthroughs in energy storage, energy conversion, and quantum sensing. But the discovery and design of new EC MOFs based on expensive experimental screening is increasingly impractical due to the infinite chemical space. Furthermore, the practical implementation of EC MOFs for specific tasks depends …

Evaluating Stormwater & Carbon Benefits Of Urban Street Trees, Anthony J. Rodriguez Diaz

Theses

Urban areas experience a multitude of environmental challenges, including flooding and air pollution. In response to these pressures, urban forests have emerged as an essential nature-based strategy to enhance resilience and reduce climate-related risks. The implementation and expansion of urban street trees further contribute to this effort by mitigating stormwater runoff and reducing atmospheric carbon emissions.

Fortunately, advances in environmental modeling have made it increasingly possible to quantify these ecosystem services using specialized software. The United States Department of Agriculture (USDA) Forest Service's i-Tree suite exemplifies this progress. The software provides a comprehensive set of tools designed to quantify environmental …

A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya

Mathematical Modelling and Numerical Simulation with Applications

Human immunodeficiency virus (HIV) continues to be a public health problem in many countries of the world, and Pre-exposure prophylaxis (PrEP) is a preventive method for HIV, which has shown great efficacy and is in use worldwide. This work presents a new mathematical model for HIV transmission incorporating PrEP use and evaluates the impact of PrEP along with its increasing use in a population. The construction of the model takes into account three forms of diagnosis: diagnosis of individuals in risky sexual contact, diagnosis after risky contact (diagnosis in the undiagnosed infected compartment), and diagnosis associated with attempting to enter …

Empowering Youth In A Changing Climate: Design, Implementation, And Evaluation Of A Salt Marsh Summer Science Program, Dan Levesque

Graduate Masters Theses

Climate change presents not only environmental challenges but also emotional challenges for today’s youth. This thesis documents the design, implementation, and evaluation of a field-based summer science program aimed at empowering adolescents with coastal salt marsh ecology while addressing climate change emotions and science identity development. The program, based in a Massachusetts salt marsh, was adapted from existing public environmental curricula and guided by place- and experience-based learning principles. Over Spring and Summer 2025, 13 students (ages 13-18) participated in extra-curricular field trips, hands-on research activities, and reflective discussions about the environment and the emotions it brings forth. Pre- and …

Information Processing In Quantum Thermodynamic Systems, Shou-I Tang

Graduate Masters Theses

This thesis extends the classical autonomous Hamiltonian framework of information thermodynamics to the quantum regime. In this formulation, a composite system consisting of a principal system, a heat bath, a memory, and a work source is described by fully quantum, time-independent Hamiltonian dynamics. By introducing the quantum speed limit (QSL) for the system and memory subsystems, referred to as the Quantum Thermodynamic Speed Limit (QTSL), I establish a connection between the QTSL and Landauer’s principle. This relationship reveals the fundamental constraints on quantum information processing in terms of dynamics and energy costs during the evolution. Furthermore, I present an interpretation …